Quantum Cryptography and

Quantum Computing

Cryptography is about

a) manipulating information b) transmitting information c) storing information

Computing is about

a) manipulating information b) transmitting information c) storing information

What fundamental concepts of quantum physics were explored in the quantum video?

a) measurement-disturbance and many worlds b) wave-particle duality and the pilot wavec) many worlds and the pilot waved) measurement-disturbance and wave-particle duality

Wave-particle duality means that a quantum object can be in two places or states at one time.

This is called a superposition and it is essential for quantum computing.

Measurement-disturbance is essential for quantum cryptography.

Entanglement is used for both cryptography and computing.

One method of cryptography uses a long random string of digits - a key - to encrypt and then decrypt a message.

The key must be random, as long as the message and it can only be used once.

Quantum Cryptography

Only quantum physics can provide truly random keys.

Quantum physics can also provide a secure way to transmit these keys.

It uses entangled polarized photons. To understand polarized photons, you just need to take your understanding of polarized light and imagine what will happen if the light is so faint, there is only one photon.

A photon has passed through a vertical polarizer. It heads towards a second one. What are the chances that the photon will be able to pass through it?

a) 0% if it is vertical and 100% if it is horizontalb) 100% if it is vertical and 0% if it is horizontal

     c) 50% if it is vertical and 50% if it is horizontal d) 100% if it is vertical and 100% if it is horizontal

A photon has passed through a vertical polarizer. It heads towards a second one. What are the chances that the photon will be able to pass through it?

a) 0% if it is +45 and 100% if it is -45b) 100% if it is +45 and 0% if it is -45

     c) 50% if it is +45 and 50% if it is -45 d) 100% if it is +45 and 100% if it is +45

A photon has passed through a vertical polarizer. It then passed through one at +45. What are the chances that the photon will be able to pass a third?

a) 0% if it is vertical and 100% if it is horizontalb) 100% if it is vertical and 0% if it is horizontal

     c) 50% if it is vertical and 50% if it is horizontal d) 100% if it is vertical and 100% if it is horizontal

Alice sends Bob a key using polarized photons.

Animation of bb84

Eve tries to eavesdrop.

• She doesn’t know what basis to use.• Suppose a vertical photon was sent and she chose

diagonal polarizers. • The value she got is meaningless and she will send

Bob a diagonal photon, not a vertical one.• If Bob uses the correct basis, he might get a

horizontal photon instead of vertical and Eve’s presence will be detected.

Suppose Eve intercepted 16,000 photons. How many times will

she get caught?1) 8,000

2) 4,000

3) 2,000

4) 1,000

Quantum Computers

Computers are based on quantum devices - transistors - which are getting smaller and smaller. Soon they will be so small that they will be directly subject to quantum rules.

This is both a problem and an opportunity. We will be looking at the opportunity.

Quantum computation is fundamentally different from classical computation.

Our present computers store information in bits, which can be either a 0 or a 1.                                        

A quantum computer stores information in qubits. These can be both a 0 and a 1 because quantum objects can be in a superposition of two states at one time.

                           

When the object is measured, it is disturbed, and is always found in one state or the other – 0 or 1.

                           

polarization spin energy level

The real power comes when you have entangled qubits. Three qubits can be in all the possible bit combinations at once; 000, 001, 010, 011, 100, 101, 110 and 111.

That’s eight pieces of data - not three. When measured, you will get one of them.

000 001 010 011 100 101 110 111. 000 001 010 011 100 101 110 111.

How many bits can you store in 20 qubits?a) 1,000b) 10,000c) 100,000d) 1,000,000

What might a quantum computer do that a classical computer can’t?

• Simulate quantum systems• Make a really fast search engine• Factor really big numbers*

* Which is why we need quantum cryptography!

To get a feeling for how quantum computation is fundamentally different from classical computation, we are going to look at quantum tic tac toe.

Superposition

1

1

Many games/calculations at a time.

1

1

1

1

1

1

2 2

1 2

1

2

1

2

Entanglement

1

1

2 2

Measurement-Disturbance

3

3

1

23 1 2

3

1

2

Random Classical States

3

1 2

3

1

2

3

4

41 2

34

1 2

34

1

2

35

51 2

345

1 2

3454

1 2

35

4

4

1

2

35

5

6

61 2

345

6

1 2

345 6

4

4

1

2

3

4

1 2

34

5

5

6

6

Weird Quantum Result

1 2

36

45

Weirder Quantum Result

http://www.paradigmpuzzles.com/QT3Play.htm

1 1

2 2

3

3

4

4

6

6

88

7 7

5

5

1

2

3

6 5

74

81

2

36

57

48