Development towards aBB84 QKD system for

CubeSats

Rajesh MishraA0119779J

Supervisor:Associate Professor Alexander Ling

Submitted for Honours Thesis

Acknowledgements

I would like to take this opportunity to express my greatest gratitude to my

supervisor, Associate Professor Alexander Ling for giving me this opportunity

to work on this project. I would also like to thank Senior Research Fellow

Robert Bedington for his continuous guidance and mentoring throughout the

two semesters.

It has been a long and amazing learning journey for me. This would not

have been possible without all the people in the lab. Really thankful to them

for sparing the time to explain to me and help me out in anyway possible. I

took up this project without much experience in optics and would like to thank

everyone again for showing so much patience and lending a helping hand. It has

been a truly enjoyable time being with the group and spending time in the lab.

Thanks to all my friends, family members and everyone else for every single

bit of encouragement and living through the moments of frustration with me!

i

Contents

Abstract iii

I Introduction 1

1. Cryptography . . . . . . . . . . . . . . . . . . . . 1

2. Why Quantum Cryptography . . . . . . . . . . . . . . 2

II Background 4

1. Quantum Key Distribution . . . . . . . . . . . . . . . 4

2. BB84 . . . . . . . . . . . . . . . . . . . . . . . 5

III Review - Advancements in Quantum Key Distribution 9

1. Challenges . . . . . . . . . . . . . . . . . . . . . 10

IV Aims 19

V Methodology 20

1. Setups . . . . . . . . . . . . . . . . . . . . . . 21

2. Device Physics . . . . . . . . . . . . . . . . . . . 27

VI Results and Discussion 31

1. Characterisation of the modulator . . . . . . . . . . . . 31

2. Estimation of Source Mean Photon Number . . . . . . . . . 33

VIIEvaluation and Conclusion 44

ii

Abstract

BB84 QKD is a method of key sharing based on the laws of quantum mechanics.

It is theoretically proven to provide unconditional security to its users. However

that is not always the case when it comes to practical cases since the equipment

used are not perfect. In this project, we have explored a configuration for

conducting QKD using a nanosatellite. The first step in the process of building

a nanosatellite based QKD is to show that such a configuration works on a

optical table and then modify it to fit in a nanosatellite.

For our setup, we have used a Vertical Cavity Surface Emitting Laser as

a source, a Thor Labs EO-AM-NR-C1 as a modulator and an avalanche pho-

todiode and a superconducting nanowire single photon detector as detectors.

The aim of this project was to characterise the source mean photon number

for our setup. In pursuit of incorporating signal and decoy states for a decoy

state quantum key distribution, source mean photon numbers of 0.247 ± 0.036

and 0.142 ± 0.023 were achieved for 14V and 0V modulation at 100kHz. Some

changes to the setup can be made to achieve a higher source mean photon num-

ber for the signal state and a higher frequency of modulation. This will allow

us to generate keys securely at a high rate.

iii

Chapter 1

Introduction

1 Cryptography

Cryptography is the art of secret writing. The word is derived from the Greek

word kryptos, meaning hidden. The simplest forms of cryptography have ex-

isted for centuries and were widely used for communication between royalty

and kingdoms. Messengers on horseback carrying letters were the most com-

mon means of communication before telegraph and other means of transport

were invented. It was not uncommon for a messenger to get kidnapped or even

murdered by groups trying to intercept the messages. Hence, cryptography was

crucial to prevent the messages from ending up in the wrong hands [1].

Advancements in the field of cryptography brought about advancements in

the field of cryptoanalysis and the cat and mouse chase has continued till today.

The attempted assassination of Queen Elizabeth in the 16th century and the

Enigma machines in the second world wars are just two of the many cases when

cryptography was used to plan the assassination and war respectively [2].

There has been a rapid improvement in the field of cryptography through-

out the 20th century and today we have many different protocols based on

complex mathematics and information science governing the exchange of digital

information. Previously, cryptography was mainly used by the military or the

governments for communication, however, today it is used in many forms of dig-

ital communications involving ordinary citizens and business. Stakes are even

higher with huge volumes of online transactions involving trillions of dollars and

pieces of sensitive information being shared with a click of a mouse [2].

1

2 Why Quantum Cryptography

Modern cryptography can be classified into two cryptosystems: symmetric and

asymmetric (public) [3]. Some of the examples of symmetric-key cryptogra-

phy are Data Encryption Standard (DES) and Advanced Encryption Standard

(AES), and some examples of asymmetric-key cryptography are Rivest-Shamir-

Adleman (RSA) and Elliptic Curve Cryptography (ECC). Both cryptosystems

are currently being used for different purposes in keeping our communications

secure, however, neither of them is fully secure and so is vulnerable to attacks.

Symmetric key encryption refers to the system where both sender and re-

ceiver have the same key. It will be secure if the key is as long as the message

and changes with each message. This is known as the one-time pad encryption

and it prevents a third party from recognising the patterns and decoding the

messages. Also, different keys are required for each pair of sender and receiver.

This process of generating and sharing keys at a fast rate acts as a limitation

for this cryptosystem and in turn can be exploited by the cryptanalysts. Asym-

metric/Public key encryption on the other hand works using a public key and

a private key. An individual can share his/her public key which is then used

by the sender to encrypt the message and this message can only be decrypted

using the corresponding private key. It is useful in digital signatures to verify

the sender’s identity. However, this encryption system has its own flaws too,

since it is based on the computational complexity of mathematical problems, for

example, RSA, which is based on the prime factorisation. For a prime factori-

sation problem, if a number is too large, there is no efficient classical algorithm

known today. With the current computational speed, solving one such problem

can take many years [4]. But with faster computers especially Quantum Com-

puters, these problems can be solved in polynomial rather than exponential time

(Figure 1.1). Algorithms such as Shor’s algorithm have shown that the RSA

encryption can indeed be broken using a Quantum Computer [5].

2

Figure 1.1: Comparison of computation time between classical and quantumcomputers [6]

Therefore, as cryptanalysts or hackers find better ways to hack the current

encryption systems, there are a lot of efforts in the direction of devising even

better encryption systems and hopefully unbreakable ones. One such idea called

Quantum Cryptography was devised in the later part of 20th century and cur-

rently a lot of efforts are being directed towards its implementation.

3

Chapter 2

Background

1 Quantum Key Distribution

Quantum Cryptography, first proposed by Stephen Wiesner in the 1970’s, ap-

plies fundamental laws of Quantum Mechanics to allow for secure symmetric key

generation [7] [8]. The most common and well-developed example of Quantum

Cryptography is Quantum Key Distribution (QKD). Unlike classical cryptogra-

phy, the security of QKD does not rely on unproven computational assumptions.

The first QKD protocol was devised by Charles H. Bennett and Giles Brassard

in 1984 and was named BB84 [9].

There are two types of QKD: prepare and measure scheme and entanglement

based. BB84 in which each qubit is encoded in one of the four states of two

complementary basis and B92 in which each qubit is encoded in one of two non-

orthogonal states are examples of prepare and measure schemes. E91 proposed

by Artur Ekert in 1991 is based on entanglement where a pair of entangled

photons are distributed to Alice and Bob [10]. For this project, the focus will

be on BB84.

QKD is unconditionally secure due to a few simple principles of Quantum

Mechanics:

• Every measurement perturbs the system.

• It is impossible to copy data encoded in a quantum state (no-cloning

theorem) [11].

4

In QKD, a quantum as well as classical channel is required to carry out com-

munication. Distribution of secret bits that will form the key is only done via

the quantum channel. Sender, usually called Alice sends qubits to the receiver,

usually called Bob. A key distillation process that is discussed in the next sec-

tion is carried out by both to retrieve the key. It is during this process that they

can know about the presence of an eavesdropper. Once the keys are distributed,

the classical channel is used by the sender to send the encrypted message to the

receiver. Therefore, the main aim of QKD is to produce and distribute the keys

which are then used for encryption.

2 BB84

The BB84 protocol is one of the best known QKD protocols and its security has

been proven by many previously. Even though it is usually implemented using

polarised photons, any two-level quantum system can be used instead.

Most commonly, two of the polarisation bases: rectilinear,diagonal or cir-

cular basis are used to produce 4 quantum states. Vertical and horizontal for

rectilinear and diagonal and anti-diagonal for diagonal (Figure 2.1) and left and

right for circular basis. For both these bases, we can attribute the binary value

of 0 to one of the states and 1 to the other state [12].

Figure 2.1: Bases states in BB84 [12]

Let’s say we have two parties: Alice and Bob. They wish to communicate

securely and to do so they need to first generate keys that will be used to encrypt

their messages and hence, they will need to carry out QKD.

5

Alice has a setup that generates qubits that correspond to individual states

prepared using one of the two bases shown in Figure 2.1. Qubits or quantum

bit are the basic unit of quantum information. In a classical system, a bit

represents either a 0 or a 1, however, in a quantum system, a qubit refers to a

coherent superposition of both the states. This idea of superposition which is a

fundamental concept in quantum mechanics allows BB84 to be unconditionally

secure.

Alice sends a string of binary numbers encoded in qubits to Bob. When this

string reaches Bob, he can carry out measurements to retrieve back the string

of binary numbers from the qubits. Bob can only retrieve the correct state if he

uses the same basis as the one used by Alice to generate that qubit. If Bob uses

the wrong basis then he will randomly retrieve a state, 50% of the time 0 and

50% of the time 1. Therefore, he will only retrieve the correct binary number

half the number of times when he chooses the wrong basis for conducting the

measurements. Using this property, Alice and Bob can identify the presence of

an eavesdropper if any.

Figure 2.2: Generation of Secret Key

Let’s assume Eve is an eavesdropper and is trying to eavesdrop on the QKD

between Alice and Bob. Referring to Figure 2.2, Alice generates a string of

bits and encodes them using randomly generated basis. Then she sends the

generated qubits to Bob through the quantum channel. Eve, who is trying

to eavesdrop, must intercept the communication and then resend the photons,

because without making a measurement on a qubit, one cannot retrieve the

information stored in it. Hence, Eve must carry out a measurement without

having any knowledge about the basis used to generate the photons. Once a

measurement is made on a qubit, it collapses to one of the 4 states. If the basis

Eve used matches the one Alice used, then Eve is lucky, and she can generate a

6

qubit using the same basis again and resend it to Bob. However, if Eve uses the

other basis, then she gets a random output and the photon that she resends is

no longer in its original state.

Bob on his side used random basis to carry out the measurements since he

has no knowledge of the basis used by Alice for generation of qubits. Once Bob

finishes his set of measurements, he shares his set of bases with Alice over an

authenticated classical/public channel. Even Eve can listen to this part of the

communication but cannot modify it. Alice and Bob discard all the bits where

their basis does not match. Now they shift their attention to the bits left.

This shorter set of bits obtained after bases reconciliation is called the sifted

key. Alice and Bob use a small segment of the sifted key obtained to check

for the presence of an eavesdropper. Ideally every single outcome compared

should match for both since the bases used are the same. Mismatch at this

point indicates that their communication has been tempered with and is most

likely due to an eavesdropper. In such a case, Alice and Bob will discard the

whole key and start over again to generate a key.

Once a key is generated, it is truly random and neither Alice nor Bob has

any control over the key that is generated. Hence, using the fundamentals of

quantum mechanics it can be proven that BB84 is completely secure against

eavesdropper attacks and if used as a one-time pad symmetric encryption key,

it is also not hackable. However, practically there are many implementation

issues that researchers need to deal with, and this has been discussed in the

next section.

2.1 Decoy-state QKD

One of the most common loopholes in the standard BB84 protocol arising due

to the unavailability of single photon sources is the presence of pulses having

multiple photons. This puts the system at risk of attacks known as photon

number splitting (PNS) attacks from the eavesdroppers, Eve [13]. PNS attacks

are those where the pulses carrying photons are transmitted from Alice to Bob

and rather than each of the pulses having single photons, they have multiple

photons. This distribution of pulses containing single or multiple photons is

unknown to Alice and Bob, so they are unable to predict which pulses contain

multiple pulses. Eve can measure the photon number of each signal and then

split the multiphoton signals. She can keep one of the photons in a quantum

7

memory for herself from these multiple photon pulses and send the others to

Bob. Since the polarisation of each of the pulses is the same, the photon/photons

reaching Bob and the photon with Eve are the same. Eve can then wait for the

measurement bases to be shared between Alice and Bob and use the information

to carry out measurements on the photons she is holding on to. This leads to

the leakage of information and Alice and Bob have no way of knowing how much

information Eve has regarding the generated key. Thus, risking the security of

the communication.

Figure 2.3: Multi-photon pulses. The orange coloured dots represent the pho-tons

Decoy state QKD was proposed in the early 2000s to counter the PNS attack

[14]. The main idea is to have a few more states in addition to the standard

BB84 states. These additional states are called the decoy states and they vary

from the standard states in their intensities. While the standard states are still

used to generate the keys, the decoy states are used to detect eavesdropping

attacks.

Figure 2.4: Decoy State QKD

8

Chapter 3

Review - Advancements inQuantum Key Distribution

Practical QKD was first demonstrated in the early 1990’s by Bennett and Bras-

sard at the IBM laboratory. The set up from that experiment in shown in Figure

3.1. QKD in this experiment was performed over a distance of 30cm [7].

Figure 3.1: First ever BB84 setup at the IBM laboratory

In 2006, a collaboration in Europe carried out QKD via an optical-free-space

link between Canary Islands of La Palma and Tenerife. This was carried out us-

ing Optical Ground Station of the European Space Agency where the observers

were separated by 144km [15]. The same group also carried out another round

of QKD in 2007 but this time using BB84 enhanced with decoy states. This was

the longest distance at that point of time. In another effort in 2007, QKD was

demonstrated by Los Alamos Laboratory and National Institute of Standards

9

and Technology over 148km of optic fibre [16]. In the same year, QKD was also

used to protect Swiss elections from hacking using an ID Quantique encryption

system.

Moving on to this decade, efforts from researcher is University of Geneva,

Coning Inc. and a few institutions from China pushed the distance to over

400kms while compromising on the secret key rate [17]. 2017 was a great year

for advancement in QKD as a group of physicists from the Institute of Quan-

tum Computing and the University of Waterloo conducted QKD from a ground

transmitter to a moving aircraft [18]. In 2017 itself, physicists from the Uni-

versity of Science and Technology of China measured entangled photons over

1203km and later successfully demonstrated BB84 over satellite links from Mi-

cius to various ground stations. This was then used to carry out a secure video

call between Beijing and Vienna [19]. There have also been efforts to minia-

turise the whole system. A group from Centre from Quantum Technologies in

Singapore aims to use CubeSats orbiting in the Low Earth Orbit to carry out

QKD between ground stations on Earth [20].

Advancements of research in QKD has also led to commercial products like

Cerberis QKD systems by ID Quantique [21]. However, there are still some

technological challenges that continue to pose a threat to the security and per-

formance of a realistic QKD system.

1 Challenges

In theory QKD allows for secure communications and this has been proven with

the assumption being that the equipment being used are perfect and behave

ideally. However, what researchers find in labs is far from ideal and these im-

perfections in the processes and in the current technologies pose threats to the

security of the system. Some of the major issues are found in photon sources

and photon detectors [12].

1.1 Photon Sources

Photon sources are broadly categorised into 3 groups: single photon sources,

coherent light sources (lasers) and thermal light sources.

QKD is based on single photon Fock states or number state. A Fock state is

10

a quantum state with a well-defined number of particles, in this case photons.

An ideal single photon source produces one-photon number states and these

number states have certain properties like photon anti-bunching. Photon anti-

bunching is a property where there is a minimum time value between successive

photons. As a result of this property, each of these photons can be used to

produce a qubit in one of the four quantum states.

In the cases of coherent and thermal light sources, there is no anti-bunching,

which means that there is a probability of multiple photons arriving in the same

time window and this can allow an eavesdropper to carry out photon number

splitting attack which will be discussed later. As of today, we still do not have

very reliable single-photon sources. But there is a lot of research being carried

out on how to use single molecules and quantum dots as single-photon sources

[22].

Most practical QKD experiments today use either faint laser pulses or en-

tangled photon pairs as the source of photons. For BB84 protocols, faint laser

pulses are the popular choice [23]. Even though they do not exhibit photon

anti-bunching, they are a good alternative when operated at low mean photon

number (μ). Since laser pulses exhibit Poisson distribution, there is well-defined

probability of finding n photons in each pulse [24]. This probability is given by

the following expression:

P (n, µ) =µn

n!e−µ (3.1)

Reducing the mean photon number reduces the probability of finding n pho-

tons in a pulse. For comparison, Figure 3.2 shows the probability of finding

a certain number of photons for different mean photon numbers. Low mean

photon number means that most of the pulses are empty and this results in a

decrease in the bit rate. Hence, this balance between the mean photon number

and the bit rate is crucial.

11

Figure 3.2: Poisson Statistics

1.2 Photon Detectors

Photon detectors are as crucial for a QKD experiment as are the photon sources.

However, in this case too we are far from having ideal single photon detectors.

Some of the common photon detectors are photo-multiplier tubes, charged-

coupled devices, photo-diodes and superconducting detectors. However, only

avalanche photodiodes (APD) and superconducting detectors are typically used

in modern QKD setups. For this project we have used both passive-quenched

APD and superconducting nanowire single photon detectors (SNSPD) for de-

tection of photons.

Some of the key characteristics of detectors are efficiency, dark counts and

dead time. Efficiency is the ratio of the number of photons the detector detects

to the number of photons arriving at the detector. Dark counts are the noise

counts that arise due to recombination occurring in the semiconductor and not

due to the photons detected. And lastly, dead time is the shortest possible

interval between the detection of two photons. It is sometimes referred to as

the recovery time if a detector. APD and SNSPD vary greatly on these 3

characteristics. The efficiency of the APD is around 50% for the near infrared.

This number varies significantly with wavelength and gain. For a SNSPD, the

efficiency can reach 90%. An APD usually has dark counts of a few hundreds

(an average of 700 for out setup) whereas an SNSPD’s dark counts are usually

less than 50. APD’s dead time is usually around 1 microsec as compared to

12

around 100nanosec for SNSPD.

Avalanche Photodiode

A photodiode is a semiconductor device that converts light into current using

the properties of semiconductors. A pure semiconductor is not desirable to be

used as a photodiode, instead it is first doped with small amounts of impurities.

Doping is used to manipulate various properties of a semiconductor for example

conductivity. This is because introduction of other elements into the semicon-

ductors causes an increase in the number of charge carriers or electrons. There

are two types of doped semiconductors, namely ‘p-type’, containing excess holes

(charge carriers) and ‘n-type’ containing excess electrons. Despite having excess

of either the electrons or holes, these semiconductors are still neutral. When a

p-type and an n-type semiconductor are in contact, diffusion of charge carriers

occur, and this leads to the formation of a p-n junction. In the p-n junction, the

excess electrons from the n-type recombine with the holes from the p-type near

the region of contact and form a depletion region. Due to this recombination, a

potential difference is generated in depletion region with the positive potential

in the n-type region and negative in the p-type region as shown in Figure 3.3.

When a photon comes and strikes the depletion region, an electron hole pair

is created. Due to the potential difference, the electron hole pair moves to the

opposite ends and results in a current in the circuit containing the diode and this

can be detected. However, the depletion region in the p-n junction is too small

for the collection of the incoming photons and hence a p-i-n junction is used

instead where, in addition to the p and n region, there is an intrinsic area which

is undoped and is added to increase the area of collection. As more photons can

be detected, it leads to an increase in efficiency.

An avalanche photodiode (APD) is a semiconductor device that also works

on the principle of photoelectric effect and its structure is like a PIN photodiode.

As the name suggests, the gain in this device occurs through the process of

avalanche multiplication. The gain depends on the applied reverse voltage. The

higher the voltage, the higher the acceleration achieved by the carriers and this

leads to the creation of more electron-hole pairs through collisions with bound

electrons. The reverse bias applied is higher than the breakdown voltage such

that even arrival of a single photon can trigger an avalanche of electrons and as

a result be detected. This mode of operation is called the Geiger mode.

13

Figure 3.3: P-N junction

The avalanche process causes a sharp increase in current in a very short

period of time and this can continue further if not stopped. In order to detect

the next photon, the diode needs to be restored to its original state where

the bias voltage is just above the breakdown. However, to stop the avalanche

process, the bias voltage needs to be lowered to below the breakdown voltage.

This quenching process can last for a period of a few nanoseconds to a few

microseconds depending on the type of quenching circuit used. There are mainly

three methods used to do the quenching: passive quenching, active quenching

and gated mode operation.

For a passive-quenching circuit, a large resistor is placed in series with the

APD. Once the avalanche starts, it causes a voltage drop across the resistor and

the voltage drop across the APD is lowered. When the voltage drop across the

APD falls below the breakdown voltage, the avalanche stops and the system

resets to detect another photon. The recovery time of a passively-quenched

detector is around 1 microsecond and this duration depends on the value of the

quench resistor and capacitor used.

For an active quench circuit, rather than waiting for the bias voltage to

14

fall below the breakdown voltage, the bias voltage is actively lowered once an

increase in current is detected. Hence, this method of operation allows for a

much faster response to the arrival of the photon and reset time is faster. As a

result, the rate of detection of photons is much higher in this case as compared

to that of the passively-quenched detector.

Lastly, for gated mode operation, the bias voltage is originally below the

breakdown and is raised above for short durations when a photon arrival is

expected. However, this needs the knowledge of the arrival times.

For this project, we have used a Silicon Geiger Mode Avalanche Photodi-

ode of SAP500-Series from Laser Components. The figure below shows the

actual APD and the form it is used in which contains the cooling system and a

discriminator circuit board.

Figure 3.4: APD from Laser Components

Figure 3.5: APD with the cooling system and discriminator card

15

Superconducting Nanowire Single Photon Detector

The technology used in the detectors has continued to improve and even though

APDs are the most popular today, there are the better performing detectors out

there. The main issues however are the cost and portability. One such type of

detector is the SNSPD. Currently, this is the fastest single photon detector for

photon counting.

A SNSPD consists of thin superconducting nanowires that are coiled in a

snake like pattern in a small area. This nanowire made of niobium nitride is

cooled to a temperature below its superconducting critical temperature and di-

rect current biased below its critical current. When a photon arrives at the

photodiode, it creates a hotspot causing the current to flow around the hotspot.

This leads to an increase in the local current density on the side beyond the crit-

ical current density and hence forming a resistive barrier (non-superconducting

region) across the nanowire. This increase in resistance from zero to a certain

value causes an output pulse to be generated and thus indicates the arrival of a

photon. The output pulse is generated due to the resistor connected in parallel

to the nanowire. When the nanowire has zero resistance, all the current passes

through it, however, when its resistance increases, there is a certain amount of

current flowing through the resistance in parallel and this leads to a voltage

drop across the resistor. Once the nanowire starts to cool and returns to the

superconducting state, the SNSPD is ready to detect another photon.

The most prominent difference between the SNSPD and the APD are the

dark count rates, efficiency and dead time. The SNSPD operates at a very low

temperature (approx. 4K) and therefore the low dark count rates in the order

of a few tens per second. The dead time is usually very low also in the order

of tens of nanoseconds. Another benefit is also the range over which these can

operate. SNSPDs can be used to detect photons in both visible and infrared

regions which is not possible using the same APD.

For this project, we have used Single Quantum Eos, a multi-channel SNSPD

from Single Quantum. The first figure below shows the principle the SNSPD is

based on and the second figure shows the detector in use in our lab.

16

Figure 3.6: Nanowire detection

Figure 3.7: Superconducting Nanowire Single Photon Detector in our lab

17

1.3 Security Loopholes

There are a few ways in which information can be leaked to an eavesdropper.

These attacks on security can be traced to either Alice’s side, which is during

the preparation, or Bob’s side, which is during the detection. Our focus for this

project is to tackle some of the loopholes on the preparation side. As discussed

above, one of the reasons to carry out decoy state is to tackle the vulnerability

caused by the presence of multi-photon pulses.

Another loophole that we have paid attention to is the issue of indistin-

guishability of lasers. This means that two VCSELS manufactured for the same

wavelength can have a frequency split in the range of gigahertz and that makes

them spectrally distinguishable. By exploiting this loophole, Eve can associate

a specific frequency with a specific polarisation state. She can then perform

a precise frequency measurement to determine the polarisation state of the in-

coming photon. A few setups for decoy state QKD have been discussed in the

next section and as we will see some of them make use of multiple lasers for

the different polarisation states and for different intensities. They might also

have slight differences due to their temperature dependence. These slight dif-

ference between the sources can lead to a leakage of information and put the

communication at a risk.

18

Chapter 4

Aims

The aim of this project was to build a table top BB84 transmitter that could

be later developed into a system for use on satellites. For this we have adopted

a compact design and chosen the components that complement the compact

design, for example, the choice of modulator. We have also chosen to use 850nm

wavelength of laser since this ensure a balance between the dispersion loss and

APD detection efficiency. Lastly, SNSPD has been used to do a cross-check on

the performance of the APD and improve the characterization of the source.

This also helped us to accurately calculate the source mean photon number.

Our project constitutes of multiple steps:

• Controlling the intensity and polarisation - this would allow us to carry

out decoy-state BB84.

• Switching the intensity and polarisation at a high frequency - this would

allow us to generate key at a high rate.

Within the time period of my final year project, I was only able to investigate

on some parts of the project. The focus was on characterizing the source of

photons for the experiment. This included the ability to control the intensity

and the mean photon number so that we can carry out decoy-state BB84 in

future and prevent security attacks such as the photon number splitting attack.

19

Chapter 5

Methodology

In the past, practical BB84 has been carried out using different setups, different

methods and different equipment. We will first discuss some of the common

ways of doing BB84 below and then dive into the setup used for this project.

But before that the choice of photon source, medium of transmission and the

method of modulation is discussed.

The first decision to be made is the one about the wavelength of the pho-

tons to be used. There are two main windows in the electromagnetic spectrum

that physicists typically use to carry out QKD: one is the near infra-red wave-

lengths (700-900nm) and the second one is the telecom wavelength bands (1300-

1600nm). These are the two windows where the loss in signal while transmission

is the least. However, both have their advantages and disadvantages. For the

near infra-red wavelengths, the detectors used are silicon based and they have a

much higher efficiency as compared to the Indium-Gallium-Arsenide (InGaAs)

ones used for the telecom wavelength. However, most optical fibre networks

are suited for telecom wavelengths since the signal suffers a much lower loss as

compared to near infra-red transmitted via optical fibre networks. A free-space

channel is rather used for the case of near infra-red. A benefit of using free-space

channel is that it preserves the polarisation of the photons but at the same time

needs an uninterrupted line-of-sight view between the transmitter and receiver.

The next task is to modulate the laser source in order to produce photon

pulses. The two different ways of modulation are direct and indirect modulation.

In the case of direct modulation, the laser source is modulated whereas in case

of indirect modulation, a continuous wave is produced by the laser diode and

20

another device is used to modulate the signal. Direct modulation is a simple and

inexpensive method as compared to the indirect one that requires an electro-

optic device which require careful setting up and are generally quite expensive.

1 Setups

The first setup discussed here uses the direct modulation technique and was

used widely in the early practical QKD experiments. The diagram is shown

below in Figure 5.1 [25].

Figure 5.1: Standard QKD setup with four laser diodes

This setup uses 4 laser diodes. Each of these laser diodes has a polariser in

front to produce the four different polarisation states. Then, using the beam

splitters the four beams are combined into one signal beam. Sometimes, rather

than using polarisers, a combination of a polarising beam splitter and half-wave

plate is used generate the states. The aim is to allow only one laser diode to

be active for each pulse. And the choice of which laser diode is active must be

completely random, hence, a quantum random number generator is usually used

for that purpose. However, this method has a drawback that can put the system

at risk. If each of the laser diodes has a slightly different spectral bandwidth,

they can be differentiated by an eavesdropper. This issue can be dealt with by

21

characterising multiple laser diodes and choosing those with similar bandwidth,

or by temperature control. For an alternative method we proposed that the

intensity of the photons could be controlled by the current supplied to the laser

diode using a current driver. Our idea was to modulate the laser diode just

above and below the threshold current of the laser diode in order to ensure a

broad spectrum that could be filtered. This approach was investigated in the

early phases of this project. This idea was dropped because tests done by our

group and other groups showed that even below the threshold current of the

laser diode, photons were produced and did not follow the Poisson distribution.

Just bringing the current down to slightly below the threshold does not work.

On the other hand, modulating the current from zero to above the threshold

at a high frequency had a limitation which is the rise and fall time due to

the capacitance in the laser driver and during those slopes, photons were also

produced, thus, preventing us from getting a good control over the mean photon

number which is essential for performing decoy state BB84 correctly.

Decoy state QKD became popular since the mid-2000s. This meathod re-

quires pulses of different intensities. One of the setups is shown in Figure 5.2

[26]. This had even more components than the previous one since it makes use

of eight laser diodes. A pair of laser diodes is used for each polarisation state

and the intensity of the pulse is determined by the amount of attenuation done

by the attenuator in front of each laser diode. Like the previous approach, beam

splitters and polarising beam splitters are used to combine the individual signal

into one channel for transmission. Decoy states are useful in tackling the PNS

attack, however, the setup was large and consisted of many components. Some

groups modified the same setup by using an electro-optic modulator instead of

directly modulating the laser diode. The setup was still bulky and expensive

since eight modulators were required.

Another group recently used a different approach for the decoy state protocol

[27]. An advantage of this design is that there is no spectral/spatial or temporal

distinguishability between the pulses because there is only a single laser being

used. The laser diode was modulated at a high frequency and then an intensity

modulator was used to generate the decoy and the signal state by varying the

voltage input to the modulator. Then a polarisation modulator was used to

encode the polarisation states. The phase was randomly chosen by a Field Pro-

grammable Gate Array (FPGA) that converted into different levels of voltage

that was fed into the polarisation modulator. The setup for this approach is

22

Figure 5.2: Decoy state QKD with multiple laser diodes

shown in Figure 5.3.

Figure 5.3: High Speed Decoy state QKD using one laser diode

For our project, an approach similar to the last one discussed has been used

whereby we make use of an 850nm vertical cavity surface emitting laser diode

(VCSEL) as compared to the Anritsu one. The VCSEL usually has a very low

threshold currect (3mA in this case) and low output power which also suggests

that less attenuation is needed. This makes it ideal for a CubeSat compatible

setup. To reduce the space used even further, we have used a Thorlabs labs

free-space modulator which is smaller than the fibre coupled ones and does not

need polarisation controllers since the free space preserves the polarisation of

photons. The free space modulator along with polarisers is used as an intensity

23

modulator and a polarisation modulator after that is used to encode the four

polarisation states. The laser is controlled using a laser driver and the intensity

modulator is controlled using a function generator which is used to provide the

modulation. Randomised switching of the voltage can then be done using a

Quantum Random Number Generator. For the detection part of the setup, an

SAP500 Silicon APD from Laser Components and SNSPD from Single Quantum

have been used to take measurements. Though SNSPD are better in every

characteristic as compared to APD, they are not practical for most QKD set-

ups. The results from both therefore have been compared as a study of whether

an APD which is portable and economical can be used as a good approximation

of a SNSPD which is bulky and expensive.

Figure 5.4: Schematic of the setup for this project

Figure 5.4 shows the schematic of set-up from our project shown in Figure

5.5. Here the VCSEL is biased using a DC current of 10.5mA. The power mea-

sured after the pinhole is ≈ 60µW. The beam then passes through the modulator

and two polarisers. Since the power measured after the second mirror is still

very high and causes the detectors to saturate, filters are placed to introduce an

24

Figure 5.5: Setup for this project. Here the VCSEL is connected to a currentdriver, the modulator is connected to the function generator and the light iscoupled into a fibre that is connected to the detector

optical attenuation of ≈ 80dB. Finally, the beam is coupled into a single-mode

fibre which is connected to the detectors.

The current setup does not contain the polarisation controller and the QRNG

since within the time period I had, we have managed to reach until this stage of

the project only. Moving forward, polarisation controller will be set-up before

the filter and both the modulators will be connected to voltage modulators which

will then be connected to the QRNG to randomly encode the signal, decoy and

the four polarisation states.

For detection of single photons, both APD and SNSPD have been used.

Upon the arrival of a photon, current flows in the circuit inside the detectors.

This causes a voltage drop across a resistor which can be detected using an

oscilloscope. A discriminator is then used to give an output as a nuclear instru-

mentation module (NIM) pulse. This is shown in Figure 5.6, where a 200mV

25

pulse is registered when a photon is detected. However, this does not allow us

to count the number of photons arriving.

Figure 5.6: NIM Pulse output from the discriminator card

Hence, a photon counting card is used (Figure 5.7). This uses a threshold

voltage and compares it with the leading edge of a pulse. If the pulse surpasses

the threshold voltage, then it is counted as a detected photon and the arrival

time can be extracted as a time-stamp. The resolution of this photon counting

card is 2ns. The time-stamps can be stored into a file and the data is processed

to find the intervals between successive photons. This can then be used to

calculate the mean photon number and the probability distribution.

Figure 5.7: Photon Counting Card

26

2 Device Physics

Before moving forward towards the discussion on the experimental procedure

and results, it is important to understand the working of the devices used in the

setup. Earlier in this report we have talked about the working of the photon

source and the photon detectors and now we will delve into the physics behind

the modulators that are used to carry out intensity and polarisation modulation

in this project.

2.1 Electro-optic Modulators

Modulators are most commonly used to vary properties of a waveform for ex-

ample, amplitude modulation or frequency modulation. In this project, we will

deal with intensity and phase modulation.

In this project, the most important part is encoding information in photons

and to do so we need to generate pulses that carry photons and encode infor-

mation in those using relative phases. To do so we need to change the phase

and hence, there is a need for modulation. As briefly discussed earlier, we can

carry out modulation either by directly modulating the source of photons or by

using external modulators.

Electro-optic modulators are a type of external modulator used to carry out

optical modulation. These modulators use the electro-optic effect to encode

information and modulate light wave carriers. This is done by altering the

optical properties of the material in a controlled way by applying voltage. These

devices use special properties of certain crystals to exhibit an electro-optic effect.

When an electric field is applied across certain crystals, there is a redistribution

of charge and a slight deformation of the lattice. These deformations are not

isotropic and vary with the direction in which the voltage is applied. Two types

of changes can occur in the impermeability tensor elements: one varying linearly

with the applied Electric field and is known as the Pockel’s effect and the other

varying quadratically is known as the Kerr effect. Most modulators are based

on Pockel’s effect.

For the light travelling through an anisotropic material, there is an ordinary

axis and an extraordinary axis and corresponding to these axes, there is ordinary

index and extraordinary index of refraction. A plane wave linearly polarised in

27

either of these two axes will remain so. However, for a wave polarised in other

directions will experience a change in their ordinary and extraordinary refractive

index, causing it to change phase as it travels through the medium.

This property of birefringence material can be used to manufacture phase

and intensity modulators. For our project we have used a free-space Electro-

optic modulator from Thor Labs that consists of a Lithium Niobate crystal and

a radio frequency input connector (Figure 5.8). This allows us to modulate the

signal up to a frequency of 100MHz.

Figure 5.8: Electro-optic Modulator (EO-AM-NR-C1) from Thorlabs

When a voltage is applied across the crystal, there is a change in the refrac-

tive indices along the ordinary and extraordinary axes. This causes a change in

the polarisation state of the light. For the modulator to work ideally, the input

polarisation state must align with the principle axis of the crystal and therefore,

a polariser is placed in front of the modulator. By just using a polariser in front,

this device acts as a polarisation modulator, generating anti-diagonal, diagonal,

left and right polarisation states. These states lie on the Bloch Sphere as shown

in Figure 5.9 [28]. Figure 5.10 shows the setup for polarisation modulation.

28

Figure 5.9: Bloch Sphere with the different polarisation states labeled on it

By placing a polariser behind the modulator, the setup for polarisation mod-

ulation can be changed into one for intensity modulation (Figure 5.11). To start

with, the polarisation axis of both the polarises is orthogonal to each other when

zero or no voltage is applied to the modulator. This is to ensure that the in-

tensity of light after the second polariser increases as we increase the voltage

supplied to it.

Figure 5.10: Polarisation modulation using an input polariser and an electro-optic modulator

The voltage required to cause a retardance of pi radiance is called Vπ. This

is equivalent of changing the intensity of the output light from the minimum to

29

Figure 5.11: Intensity Modulation using an electro-optic modulator between twopolarisers

the maximum. The graph of the transmittance of light as a function of voltage

is shown in Figure 5.12. It also shows that there is a sine squared dependence

of intensity on the applied voltage.

Figure 5.12: Transmission vs Voltage Curve for an ideal Intensity Modulator

30

Chapter 6

Results and Discussion

For this project, the focus was to understand what the mean photon number is

and how it is accurately calculated in QKD systems. This is necessary to verify

systems that will allows us to control the mean photon number such that we

can implement decoy state QKD on a CubeSat scale in the future.

1 Characterisation of the modulator

Earlier we have discussed the workings of the electro-optic modulators. Here,

we explore the details to get a better idea of the performance of our modulator

before using it to carry out intensity modulation. The same amplitude modu-

lator can be used for a range of wavelengths from 600-900nm but the halfwave

voltage varies with the wavelength. The simplified expression is given in the

manual as:

Vπ = 0.361λ− 23.844 (6.1)

where λ is the wavelength of the light.

Using this, the Vπ for 850nm can be calculated as 283V.

A miniature APD power supply (ultra-compact PCB mountable) from Mat-

susada Precision (TS-0.3P) has been used together with a potentiometer to do

a voltage sweep from 0-300V. The results are shown in the graph below.

The counts here refers to counts per second (cps) detected using an APD

31

Figure 6.1: Photon Counts vs Voltage graph for the modulator. The scatter plotrefers to the measured data and the solid line refers to the theoretical sin2 π2

VVπ

curve from Figure 5.12

when the laser diode is illuminated. The max count in this case is 375000 and

the minimum is 4500, giving an extinction ratio of 19.2dB. Extinction Ratio is

the ratio of two extreme power levels in a signal generated by a optical source.

This is property of the modulator and is dependant on its alignment with the

input beam.

ExtinctionRatio = −10 logMax

Min(6.2)

The maximum and minimum counts change upon changing the attenuation,

but the extinction ratio fluctuation is negligible. The modulator works ide-

ally when the polarisation of the input beam matches the principle axis of the

Lithium Niobate crystal inside the modulator. The polariser in front of the

modulator is used to alter the input polarisation and the mount on which the

modulator sits is used to change the orientation of the base plane to allow for

maximum amount of light to be coupled into the crystal. In an ideal scenario at

zero voltage, the cps should be equal to the dark counts since the crystal does

not change the phase of the beam and with the polarisers orthogonal to each

32

other, they do not allow any photons to pass through.

2 Estimation of Source Mean Photon Number

As introduced before, the aim is to be able to control the mean photon number

of the source. This is the mean photon number corresponding to the photons

prepared by Alice. For QKD, these are then transmitted from Alice to Bob.

The statistics of these photons can be acquired by doing measurements on

them, in this case detecting them using an APD or a SNSPD. However, the result

obtained from the detector is referred to as detected mean photon number (µdet)

and this is usually much less than the source mean photon number (µsource).

In order to acquire the source mean photon number, the detected mean pho-

ton number needs to be corrected for detection efficiency (η) and the dead time

(τ). In this project, we have used an APD and two channels of the SNSPD

to carry our measurements and observe the trends. The efficiencies of the two

channels of the SNSPD are known and this has been used to estimate the effi-

ciency of the APD. The final result obtained is an average of the three and is

discussed in detail later.

2.1 Dead Time Correction

For all counting devices, there is minimum amount of time that is necessary to

resolve two different events. When one event is being processed and the system

has not recovered to its original state, another event occurring during that time

period is either not registered or there is a pile up leading to a longer recovery

time. Due this this effect, the experimental statistical distribution deviates from

the theoretical one and corrections are needed to process the collected data. The

model that the setup follows depends a lot on the type of discriminator card

being used.

There are two types of dead time models and they vary with respect to the

effect that an event occurring within the dead time of the previous event has on

the system [29]:

• Non-paralysable/non-extendable dead time: In this model, an event oc-

curring within the dead time of the previous one is not accounted for.

33

• Paralysable/extendable: In this model, the occurrence of an event within

the dead time of the previous one causes the dead time to extend by a

period of τ from the point of occurrence of the second event.

Figure 6.2 diagrammatically explains the two models.

Figure 6.2: Extendable and Non-extendable Dead time models [30].

Due to the different behaviour in the two models, the output rate also varies

for both. As can be seen in Figure 6.3, the two models behave the same for

low intensities/low counts as there is less likelihood of events occurring withing

the dead time window. However as the intensity increases, the output counts

from the two models diverge. This is because for the extendable model, the

dead time period extends due to pile up of counts and fails to capture as many

counts as the non-extendable model. This becomes more and more severe with

the increase in the intensity. But for the non-extendable case, the counts increase

until a saturation point where once the detector exits the dead time window, it

immediately registers a count and hence the saturation counts is determined by

1/τ .

The APD used in our project exhibits an extendable dead time model

whereas the SNSPD used in our project exhibits a non-extendable model. How-

ever, since the range of counts in which our setup is operated is far below the

extendable saturation counts (1/τe), we use the non-extendable equations which

are simpler and can be used for correcting the data from both the detectors.

34

Figure 6.3: Output vs Input count rates for the two models [30].

The saturation counts for the APD is around 470000 and for the SNSPD is

approximately 3700000 while for all our measurements, the counts have been

kept below 40000.

• Poisson Distribution:

P (n, µ) =µn

n!e−µ (6.3)

• Poisson Distribution for non-extendable dead time model [31]:

P (n, µ, τ) =

n∑k=1

µn

(Tn)k!(T − nτ)

ne(−µ+

µT nτ)

−n−1∑k=1

µn

(Tn)k!(T − (n− 1)τ)

ne(−µ+

µT (n−1)τ)

(6.4)

where µ is the corrected mean photon number, n is the detected counts

and T is the duration of the pulse.

• Mean Photon Number for the above model:

n′

= µ(1 +µ

Tτ)−1 + 0.5(

µ

Tτ)2(1 +

µ

Tτ)−2 (6.5)

35

• Variance:

σ2 = µ(1 +µ

Tτ)−3 (6.6)

In order to obtain µ, we need to solve (6.5), which can be simplified into a

quadratic equation with the root being µ.

µ =−(2n

′t− 1) ±

√(2n′t− 1)2 − 4(n′t2 − t− t2

2 )n′

2(n′t2 − t− t2

2 )(6.7)

where t = τT

For our measurement, we have chosen to produce laser pulses at a frequency

of 100kHz since dead time limits the frequency that we can use for our detectors.

Even though we can use higher frequencies for SNSPD, but 100kHz is a value

where both the detectors work well. The time period for a 100kHz square wave

is 10µs and a 50% duty cycle gives T = 5µs.

In the case of APD, t = 0.2 and the corrected mean photon number is given

by:

µ =−(0.4n

′ − 1) −√

(0.4n′ − 1)2 − 4(0.04n′ − 0.22)n′

2(0.04n′ − 0.22)(6.8)

In the case of SNSPD, t = 0.02 and the corrected mean photon number is

given by:

µ =−(0.04n

′ − 1) −√

(0.04n′ − 1)2 − 4(0.0004n′ − 0.0202)n′

2(0.0004n′ − 0.0202)(6.9)

The difference between the two mean photon numbers depends on the in-

tensity of the input light and on the value of τT . A higher intensity results in a

larger value of n′

and as a result a larger correction. The same trend applies to

the values of τT .

Since in our case, we are operating at a very low intensity and τT is not very

high, the corrections are small but still can’t be ignored.

36

Voltage Detected Mean Corrected Mean Difference

0 0.061 0.062 0.0012 0.064 0.065 0.0014 0.065 0.066 0.0016 0.068 0.069 0.0018 0.071 0.072 0.00110 0.078 0.079 0.00112 0.087 0.088 0.00114 0.101 0.103 0.002

Table 6.1: Corrections to the Detected Mean Photon Number for APD

Voltage Detected Mean Corrected Mean Difference

0 0.0877 0.0879 0.00022 0.0887 0.0889 0.00024 0.0911 0.0913 0.00026 0.1011 0.1013 0.00028 0.1111 0.1113 0.000210 0.1200 0.1203 0.000312 0.1403 0.1407 0.000414 0.1550 0.1555 0.0005

Table 6.2: Corrections to the Detected Mean Photon Number for SNSPD (Chan-nel 1)

Voltage Detected Mean Corrected Mean Difference

0 0.0561 0.0562 0.00012 0.0579 0.0580 0.00014 0.0615 0.0616 0.00016 0.0645 0.0646 0.00018 0.0703 0.0704 0.000110 0.0797 0.0798 0.000112 0.0898 0.0900 0.000214 0.1009 0.1011 0.0002

Table 6.3: Corrections to the Detected Mean Photon Number for SNSPD (Chan-nel 2)

2.2 Detector Efficiency

Detection efficiency refers to the ratio of the number of photons detected by the

detector to the number of photons reaching the detector. The correction for the

37

detection efficiency η is rather simple.

µsource =µdet

′

η(6.10)

The detection efficiency of the SNSPD Channel 1 and Channel 2 are known to

be 57%±5% and 40%±5% respectively from callibration report. Data collected

for the two channels and the APD was used together with the knowledge of the

SNSPD efficiencies to calculate the detection efficiency of the APD. Dividing the

values of the two channels with their respective efficiencies produces the mean

value per 10µs for the source which is operated as a continuous wave. This is

then used to calculate the detection efficiency of the APD (ηAPD).

ηAPD = 47.2% ± 9.4%

.

2.3 Analysis of the modulation

An important aspect of photon pulses is the pulse width, it is ideal to have the

pulse width as small as possible, that allows one to reduce the probability of

having more than one photon per pulse but this also reduces the key rates. We

investigated the pulse width by varying the duty cycle of the pulses generated.

The pulse width of 50%, 20% and 5% duty cycle are 5µs, 2µs and 500ns. Re-

ducing the pulse width however comes at a penalty of reducing the dynamic

range of the attainable mean photon numbers.

Figure 6.4: Photon counts vs time for 50% Duty cycle modulation. Graph onthe left shows the counts for 4V peak to peak modulation. Graph on the rightshows the counts for 2V peak to peak modulation. Area is grey is the changein counts for each pulse when the voltage is changed

38

Figure 6.5: Photon counts vs time for 20% Duty cycle modulation. Graph onthe left shows the counts for 4V peak to peak modulation. Graph on the rightshows the counts for 2V peak to peak modulation. Area in grey is the changein counts for each pulse when the voltage is changed.

Figure 6.4 and 6.5 are a way to visualise the modulation and change in duty

cycle and how it affects the counts and eventually the mean photon number.

As we can see here, the 10000 counts per second is the counts we have when

no voltage is supplied to the modulator. When a square wave pulse is supplied

to the modulator, the counts are also modulated similarly causing the above

waveforms. At the same time, the graphs also show the effect of the change of

duty cycle from 50% to 20%. Ideally if the base value was zero, then doubling

the voltage from 2V to 4V should double the area in each pulse and hence

double the counts too. This then leads to a doubling of the mean photon

number. However, as we see in Figure 6.4 and 6.5, that is not the case, and this

is because the majority of the area is due to the base value which is 10000 and

the contribution due to the change in voltage is significantly less. Furthermore,

when the duty cycle is reduced, the change in counts is even less significant

due to the modulation. Therefore, a significant drop in the range of the mean

photon number when the modulation is changed from 50% to 5%. Also, at low

duty cycles, the signal to noise ratio is vary low and that prevents a clear trend

between the photon counts and voltage being observed.

39

2.4 Corrections and Curve Fitting

Timestamps were collected for both the detectors and the data was used to

calculate the detected mean photon number. After that dead time corrections

and detection efficiency were accounted for to produce the actual data directly

correlated to the source. The plots for both APD and SNSPD has been shown

below.

Figure 6.6: Detected and Corrected Mean photon number vs Modulation Volt-age for APD. Correction have been made for efficiency and dead time.

Figure 6.7: Detected and Corrected Mean photon number vs Modulation Volt-age for SNSPD Channel 1. Correction have been made for efficiency and deadtime.

40

Figure 6.8: Detected and Corrected Mean photon number vs Modulation Volt-age for SNSPD Channel 2. Correction have been made for efficiency and deadtime.

From the graph we observe that mean photon number in each case follows

an increasing trend as the voltage is increased but they differ slight in the extent

of increase. For the APD, there is an increase in mean photon number from

0.132 ± 0.028 to 0.218 ± 0.045. For the Channel 1, this range is from 0.154 ±0.017 to 0.273 ± 0.027 and lastly for Channel 2, the range is from 0.140 ± 0.022

to 0.253 ± 0.023. The large error bars are a combination of the error arising

from the detection measurements and also from the error in the values of the

detection efficiencies. Graph in Figure 6.9 shows the comparison between all the

three for the corrected mean photon number. Corrected mean photon number

corresponds to the source mean photon number.

Ideally, all the three curves should match since the source mean photon

number stays fairly constant through out the experiment. However, there is

variation from the detector to detector and this can be attributed to the error

and also to differences in losses in each case. The graphs of the two channels

of SNSPD in Figure 6.9 seems to be following a similar trend which is slightly

different from that of the APD. This can be attributed to the fact that the two

channels use similar type of fibre as well as the length to couple the light from

the setup to the detectors. This is different from that of the APD. Therefore,

an average of all three has been taken to obtain the best match for the source

mean photon number. This is shown in Figure 6.10.

41

Figure 6.9: Source Mean Photon number comparison between the three detec-tors

Figure 6.10: Source mean photon number obtained using the average of thethree detectors.

Equation 6.11 have been used in Figure 6.10 to carry out the curve fit.

y = a1 sin2 π

2

V

Vπ+ b1 (6.11)

where the values of a1 and b1 were found to be 17.09 and 0.14 respectively.

From Figure 6.10, we observe that a source mean photon number of 0.142 ±0.023 and 0.247 ± 0.036 is achieved at 0V modulation and 14V modulation.

42

From equation (6.11), we know that a1 + b1 = Max and b1 = Min. There-

fore, the ExtinctionRatio = 20.9. The deviation of this value from 19.2 stated

above is due the large uncertainties in the efficiencies of the detectors.

Since the aim is to conduct decoy state QKD, it is necessary to have one or

multiple decoy states. Researchers have shown that the security of the system

improves with more decoy states but having two types of decoy states especially

vacuum and another states is a good approximation for infinite number of decoy

states [32]. The intensities of the decoy states are optimised to achieve maximum

key rates for specific wavelength and losses. Due to time constraints, we could

not conduct the optimisation and aimed to achieve a signal mean photon number

of ≈ 0.48 and decoy state mean photon number of ≈ 0.12. The higher signal

state can be achieved by applying a modulation of a higher voltage and using

the expression obtained, this voltage can be calculated to be ≈ 25V.

43

Chapter 7

Evaluation and Conclusion

With a goal of sharing keys as securely as possible though BB84 QKD, it is

extremely important to understand the constraints on the key components of

the setup and the best available alternative. In this project, we have explored a

configuration for conducting QKD where the source is on a nanosatellite revolv-

ing in a orbit around the Earth. This part of the setup consists of the source

of photons which is the laser and also parts encode the information which is an

equipment able to modulate the laser. The detection part of the setup is on the

ground and it can make use of the different types of detectors available.

One of the main constraints that we have explored in this project is space.

There are a few ways of doing decoy state BB84 as discussed earlier, but the

key was to use one the most space effective configuration consisting of the one

source, one modulator for intensity control and one for polarisation control

together with the electronics on printed circuit boards.

For our source of photons, we have used a VCSEL with a very low threshold.

This helps to reduce the power requirements of the setup which is a key factor

for nanosatellite missions and also allows us to operate it by a relatively simpler

laser driver circuit. Since we are using only one laser, we do not need to be

concerned about it being distinguishable of the photons generated. Having

multiple lasers requires the setup to have temperature control units to ensure

the that the spectra of the lasers overlap well.

Another important consideration is the choice of the modulator. There are

two types of Electro-optic modulators: pockels cell based and wave-guide based.

44

We chose the one based on pockels cell due to its smaller size. Even though the

waveguide ones are not that big but they require a temperature control and that

makes them large and bulky. One of them is show in Figure 7.1.

Figure 7.1: Intensity Modulator based on Mach Zehnder interferometry. The topsilver part contains the modulator. The box at the bottom is the thermoelectriccooler.

Even though the waveguide ones are not space efficient, they have a lot of

advantages and therefore are the common type of modulator used in most QKD

experiments. The Vπ for these modulators are usually less than 10V and hence

it is possible to do relatively large intensity modulation using these as compared

to the Pockels cells one whose Vπ is very large. Using a waveguide modulator

can help us achieve a much larger contrast between the signal and decoy states by

modulating over a small voltage. This will also allow us to operate at frequencies

of 100MHz or above. A high frequency in QKD experiments is necessary to

achieve a good key-rate generation. Another important consideration is the

duty cycle as well as pulse-width. Due to a low signal to noise ratio, we were

not able to carry out meaningful measurements using narrow pulse-width, but

this is definitely possible using the waveguide modulators. A pulse width of

5µs was used which was not ideal for any QKD system. Pulse width in the

45

range of pico-seconds and duty cycle ≤ 1% is generally used in order to keep

the communication as secure as possible [33].

The last component which is very crucial is the detector. These are on the

ground to receive the signal coming from the source. For our project, we have

used an APD whose dead time is in the order of 1µs and hence a frequency

of 1MHz is the limit. Since our aim was to study the mean photon number

using the different detectors and use them to characterise the source, all the

three detectors had to be operated using the same settings. Moving forward,

the next step will definitely be to study the mean photon number at higher

frequencies using the SNSPD or even better detectors with smaller dead time.

Though SNSPD is much better in terms of performance and is a viable option

for a scientific experiment, it is not ideal for real world implementation since

it is much more expensive and bulky as compared to an APD with an active

quenching circuit that have dead time of a few nano-seconds also [34].

In conclusion, the combination of equipment used in this project may not

be best suited for a nanosatellite compatible setup. Moving forward, it will be

important to find the balance between performance and the constraints of the

project.

46

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