Multi-user quantum key distribution with a semi-conductor ...
Transcript of Multi-user quantum key distribution with a semi-conductor ...
Multi-user quantum key distribution Multi-user quantum key distribution with a semi-conductor source of with a semi-conductor source of
entangled photon pairsentangled photon pairs
C. Autebert1, J. Trapateau2, A. Orieux2, A. Lemaître3, C. Gomez-Carbonell3, E. Diamanti2, I. Zaquine2, and S. Ducci1
1 Laboratoire MPQ, Université Paris Diderot, Sorbonne Paris Cité, CNRS-UMR 7162, Paris2 LTCI, CNRS, Télécom ParisTech, Université Paris-Saclay, Paris3 Centre de Nanosciences et de Nanotechnologies, CNRS/Université Paris Sud, UMR 9001, Marcoussis
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 01/22
arXiv:1607.01693
I/ QKD, why BBM92?
II/ Practical integrated sources for QKD:AlGaAs source of entangled photon pairs at Telecom wavelength
III/ Optimising the use of quantum ressources:Multi-user entanglement distribution with DWDM techniques
IV/ Set-up & Experimental results
V/ Perspectives
OutlineOutline
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I/ Quantum Key DistributionI/ Quantum Key Distribution
• BB84 → QKD with single photons: non-commutation of σz and σx
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H
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t1t2t3t4t5t6t7
attenuated laser diodes (cheap single photons)single-photon detectors (expensive...)limited distance (losses/noise)lots of hardware-related attacks
C.H. Bennett & G. Brassard, Proc. IEEE Comp., Syst. & Signal Process. 175, 8 (1984).
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entangled photon sources (expensive?)single-photon detectors (expensive...)increased distance (less sensitive to losses/noise)towards device-independent security
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I/ Quantum Key DistributionI/ Quantum Key Distribution
• BBM92 → QKD with photon pairs: entanglement (& non-locality)
??
?t1t2t3
C.H. Bennett, G. Brassard & N.D. Mermin, Phys. Rev. Lett. 68, 557-559 (1992).
|Ψ⟩AB
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+/–?
??t1 t2 t3
quantum server
|Ψ⟩AB = =|HV⟩ – |VH⟩
√2
|+–⟩ – |–+⟩
√2
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II/ Practical integrated sources for QKDII/ Practical integrated sources for QKD
E. Diamanti, H.-K. Lo, B. Qi & Z. Yuan, arXiv:1606.05853, Review (2016).A. Orieux & E. Diamanti, arXiv:1606.07346, to appear in J. Opt. – Topical Review (2016).
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• wide deployment of QKD → need for cheap, easy-to-operate systems
∘ standard Telecom/computing components∘ mass-manufacturing possibilities∘ room temperature operation∘ alignment-free operation∘ ...
• integrated photonics platforms:
∘ silicon (CMOS)∘ III-V semiconductors: InP, AlGaAs...∘ dielectric crystals (LiNbO3, KTP...)∘ glass
1 transistor
109 transistors
II/ AlGaAs sourceII/ AlGaAs source
• Huge χ(2) for spontanteous parametric down-conversion (SPDC)
ωA
ωBωp
n(AlGaAs) ≃ 3.0-3.5 VS n(PPLN) ≃ 2.2dχ(2)(AlGaAs) ≃ 100 pm/V VS dχ(2)(PPLN) ≃ 20 pm/V
∎ SPDC efficiency: ηSPDC ∝ L.(dχ(2))2
⇒ ηSPDC(AlGaAs) ≃ 25×ηSPDC(PPLN)⇒ mm-long VS cm-long vaveguides
L
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ħωp
ħωA
ħωB
E
II/ AlGaAs sourceII/ AlGaAs source
• energy conservation: Δ[ħω] = 0ωA + ωB = ωp (with ωA ≤ ωB)
• phase-matching (momentum conservation): Δ[ħk] = Δ[ħnω/c] = 0n(ωA)ωA + n(ωB)ωB = n(ωp)ωp
⇒ n(½ωp) = n(ωp)
• SPDC, different phase-matching techniques
n
ωωp0 ½ωp
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II/ AlGaAs sourceII/ AlGaAs source
• phase-matching (momentum conservation): Δ[ħk] = Δ[ħnω/c] = 0
quasi-PM: n(½ωp)ωp = n(ωp)ωp – 2πc/ΛQPM
→ periodic poling of AlGaAs (still technologically challenging)
• SPDC, different phase-matching techniques
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ΛQPM
z
II/ AlGaAs sourceII/ AlGaAs source
• phase-matching (momentum conservation): Δ[ħk] = Δ[ħnω/c] = 0
quasi-PM: n(½ωp)ωp = n(ωp)ωp – 2πc/ΛQPM
→ periodic poling of AlGaAs (still technologically challenging)
birefringent PM: nTE(½ωp) = nTM(ωp)→ insertion of Al-Oxyde layers (fragile material)
• SPDC, different phase-matching techniques
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TEn
ω
TM
ωp0 ½ωp
ΛQPM
z
zTE
TM
II/ AlGaAs sourceII/ AlGaAs source
F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014).C. Autebert et al., Optica 3, 143-146 (2016).
TE00
TM00
TEBragg
transverse modes:
• energy conservation:ωA + ωB = ωp (with ωA ≤ ωB)
• phase-matching (modal, type II):nTE00(ωA)ωA + nTM00(ωB)ωB = nTEBragg(ωp)ωp (1)nTM00(ωA)ωA + nTE00(ωB)ωB = nTEBragg(ωp)ωp (2)
TE⇔H
TM⇔V
z
• SPDC, modal phase-matching technique
TE00n
ω
TM00
TEBragg
ωp
ωA
0ωB
½ωp
Bragg mirrorscore layer
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II/ AlGaAs sourceII/ AlGaAs source
F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014).
TE00
TM00
TEBragg
transverse modes:
• Direct bandgap semi-conductor → electrical injection of the Bragg mode
laser diode & non-linear crystal with the same waveguide⇒ no need for an external pump laser
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II/ AlGaAs sourceII/ AlGaAs source
• Direct polarization Bell state generation over a large bandwidth
λp (nm)
λ A,B
(nm
)λ A
,B (
nm) λ A
,B (
nm)
intensity (a.u.)
TE00
TM00
λp = 778.68 nm
≃ 30 nm
TE00
TM00
|ΨA,B⟩ =|HV⟩ + eiφ|VH⟩
√2
very small birefringence⇒ no need for walk-off compensation nor interferometric schemes
|V,ωB⟩|H,ωA⟩
ωp
|H,ωB⟩|V,ωA⟩
ωp
or
F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014).
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III/ Ressource optimisation – DWDMIII/ Ressource optimisation – DWDM
• Dense Wavelength Division Multiplexing (DWDM)
ITU 100 GHz grid01 ↔ 1577.03 nm02 ↔ 1576.20 nm03 ↔ 1575.37 nm… 71 ↔ 1521.02 nm72 ↔ 1520.25 nm73 ↔ 1519.48 nm
1 long-distance SMF fiber ⇔ 73 channels
DEMUXDEMUX
0.8 nm (100 GHz)
MUX
Internet server
73 la
ser
diod
es
neighbourhoodInternet access
73 homes
→ a single fiber deployed for many users
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III/ Multi-user entanglement distributionIII/ Multi-user entanglement distribution
• Dense Wavelength Division Multiplexing (DWDM)
1 entanglement source ⇔ 36 channel pairs
J. Trapateau et al., J. Appl. Phys. 118, 143106 (2015).
DEMUXDEMUX|Ψ⟩ Alice 1Alice 2Alice 3
Bob 3Bob 2Bob 1
…
…
0.8 nm (100 GHz)
→ distribution of entangled photon pairs between symmetric channels around the degeneracy wavelength→ a single source for many pairs of users
ITU 100 GHz grid01 ↔ 1577.03 nm02 ↔ 1576.20 nm03 ↔ 1575.37 nm… 71 ↔ 1521.02 nm72 ↔ 1520.25 nm73 ↔ 1519.48 nm
quantumInternet server
72 SMF fibers
72 clients⇔ 36 pairs of clients
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III/ Multi-user entanglement distributionIII/ Multi-user entanglement distribution
• DWDM & large-band frequency anti-correlation
intensity (a.u.)
TE00
TM00
λp = 778.68 nm
≃ 30 nm
ωA
ωB
25
25
ωB = ωp – ωA
JSI(A,B)(narrow-linewidth pumping)
→ 16 pairs of channels/users available over the 30-nm bandwidth of the entangled pairs
08
42≃ 15 nm
≃ 15 nm
08 ↔ 1571.24 nm25 ↔ 1557.36 nm42 ↔ 1543.73 nm
λB
λA
25
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III/ Multi-user entanglement distributionIII/ Multi-user entanglement distribution
• DWDM & large-band frequency anti-correlation
ωA
ωB
25
25
24
26
23
27
22
28
21
29
ITU 100 GHz grid:
21 ↔ 1560.61 nm22 ↔ 1559.79 nm23 ↔ 1558.98 nm24 ↔ 1558.17 nm25 ↔ 1557.36 nm26 ↔ 1556.55 nm27 ↔ 1555.75 nm28 ↔ 1554.94 nm29 ↔ 1554.13 nm
ωB = ωp – ωA
JSI(A,B)(narrow-linewidth pumping)
→ 4 pairs of channels/users in our experiment (8+1 channels DWDM)
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IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
quantum server
Alice 23
CW Ti:salaser
778.68 nm
holographicmask 63x
Peltiercooler
AlGaAswaveguide
10x
long-pass filter
SMF collimator
DWDM
A22A21
A24
polarizationcontroller
λ/2 PBS
APD
fiber links
time coincidence
counter
Bob 27
B26
B28B29
polarizationcontroller
λ/2PBS
APD
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 16/22
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IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
• BBM92 protocol:
C.H. Bennett, G. Brassard & N.D. Mermin, Phys. Rev. Lett. 68, 557-559 (1992).X.F. Ma, C.-H.F. Fung & H.-K. Lo, Phys. Rev. A 76, 012307 (2007).
? ? ?t1t2t3
|Ψ⟩AB
H/V
+/–
???t1 t2 t3
quantum server
❶ local basis choices & coincidence measurements→ Rraw
❷ basis reconcilliation (sifting)→ Rsift = ½Rraw
|Ψ⟩AB = |HV⟩ – |VH⟩
√2|+–⟩ – |–+⟩
√2=
t1
AB
00
t2
AB
+0
t3
AB
+–
t4
AB
1–
t5
AB
–+
t6
AB
0+
t7
AB
10
00 01 1010❷
❶
t8
AB
+1
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IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
• BBM92 protocol:
C.H. Bennett, G. Brassard & N.D. Mermin, Phys. Rev. Lett. 68, 557-559 (1992).X.F. Ma, C.-H.F. Fung & H.-K. Lo, Phys. Rev. A 76, 012307 (2007).
? ? ?t1t2t3
|Ψ⟩AB
H/V
+/–
???t1 t2 t3
quantum server
❶ local basis choices & coincidence measurements→ Rraw
❷ basis reconcilliation (sifting)→ Rsift = ½Rraw
❸ error estimation (QBER) & correction→ e & f(e)
❹ secret key extraction→ Rkey ≥ Rsift( 1 – f(e)H2(e) – H2(e) )with H2(x) = – x.log2(x) – (1–x).log2(1–x)
|Ψ⟩AB = |HV⟩ – |VH⟩
√2|+–⟩ – |–+⟩
√2=
t1
AB
00
t2
AB
+0
t3
AB
+–
t4
AB
1–
t5
AB
–+
t6
AB
0+
t7
AB
10
00 01 1010
01 01 1010
0 1❹
❸
❷
❶
t8
AB
+1
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0
IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
Cfalse Cmin Cfalse Cmax
• Coincidence histograms for A23–B27 over 50 km:
→ e = ½(1 – V)V = ∑Cmax – ∑Cmin
∑Cmax + ∑Cmin
Rsift = ∑Cmax + ∑Cmin
τhisto
E. Waks, A. Zeevi & Y. Yamamoto, Phys. Rev. A 65, 052310 (2002).
Rfalse = ∑Cfalse
τhisto
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IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
• BBM92-QKD results VS distance:
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 19/22
set-up parameters:- collection efficiency: ηcol = 5%- fiber losses: α = 0.22 dB/km
- detection efficiency: ηdet = 20%- spurious count probability: d = 4.4x10-6
- polarization error (PMD): b = 6%
IV/ Multi-user BBM92-QKD experimentIV/ Multi-user BBM92-QKD experiment
• There is room for improvement (higher rates & longer distance):
- AR coating & laser-diode-to-SMF packaging→ collection efficiency ×4
- superconducting detectors→ detection efficiency ×4→ no dark counts
- no use of PM fibers→ polarization error – 3%
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 20/22
realistic improved parameters:- collection efficiency: ηcol ≥ 21%- fiber losses: α ≤ 0.22 dB/km
- detection efficiency: ηdet ≥ 87%- spurious count probability: d ≤ 2x10-6
- polarization error (PMD): b ≤ 2.5%
V/ PerspectivesV/ Perspectives
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 21/22
• Electrical pumping & chip-to-fiber packaging→ fully integrated source
• Use of 40-channel DWDM & active switches→ 20 pairs of users per source
+ quantum repeaters+ cheaper single-photon detectors+ (measurement-)device-independence
→ practical QKD fiber network
question timequestion time
QuPa – jeudi 7 juillet 2016 – Adeline Orieux 22/22
arXiv:1607.01693