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


H/V

+/–

I/ Quantum Key DistributionI/ Quantum Key Distribution

• BB84 → QKD with single photons: non-commutation of σz and σx

01

11

01

1

H

V

–

+

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).


entangled photon sources (expensive?)single-photon detectors (expensive...)increased distance (less sensitive to losses/noise)towards device-independent security

H/V

+/–

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

H/V

+/–?

??t1 t2 t3

quantum server

|Ψ⟩AB = =|HV⟩ – |VH⟩

√2

|+–⟩ – |–+⟩

√2


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).


• 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


ħωp

ħωA

ħωB

E


• 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



• 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)



ΛQPM

z


• 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)



TEn

ω

TM

ωp0 ½ωp

ΛQPM

z

zTE

TM


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



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



• 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).


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


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



• 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



• 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)


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


H/V

+/–


• 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


H/V

+/–


• 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


0


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



• BBM92-QKD results VS distance:


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%


• 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%


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


• 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


arXiv:1607.01693

Multi-user quantum key distribution with a semi-conductor ...

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