Multi-user quantum key distribution with a semi-conductor source of entangled photon pairs

Multi-user quantum key distribution with a semi-conductor source of entangled photon pairs C. Autebert1, J. Trapateau2, A. Orieux2, A. Lemaître3, C. Gomez-Carbonell3, E. Diamanti2, I. Zaquine2, and S. Ducci1 arxiv:1607.01693 1 Laboratoire MPQ, Université Paris Diderot, Sorbonne Paris Cité, CNRS-UMR 7162, Paris 2 LTCI, CNRS, Télécom ParisTech, Université Paris-Saclay, Paris 3 Centre de Nanosciences et de Nanotechnologies, CNRS/Université Paris Sud, UMR 9001, Marcoussis 01/22

Outline 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 02/22

I/ Quantum Key Distribution BB84 QKD with single photons: non-commutation of σz and σx H/V H V + 1 t7 0 t6 1 t5 1 t4 0 t3 1 t2 1 t1 +/ 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). 03/22

I/ Quantum Key Distribution BBM92 QKD with photon pairs: entanglement (& non-locality) H/V H/V quantum server +/ t1 Ψ AB t2 t3 Ψ AB = t3 HV VH 2 = t2 t1 +/ + + 2 entangled photon sources (expensive) single-photon detectors (expensive...) increased distance (less sensitive to losses/noise) towards device-independent security C.H. Bennett, G. Brassard & N.D. Mermin, Phys. Rev. Lett. 68, 557-559 (1992). 04/22

II/ Practical integrated sources for QKD wide deployment of QKD need for cheap, easy-to-operate systems 1 transistor 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 109 transistors 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). 05/22

II/ AlGaAs source Huge χ(2) for spontanteous parametric down-conversion (SPDC) n(algaas) 3.0-3.5 dχ(2)(algaas) 100 pm/v VS VS n(ppln) 2.2 dχ(2)(ppln) 20 pm/v ωa ωp L ωb E ħωa SPDC efficiency: ηspdc L.(dχ(2))2 ħωb ηspdc(algaas) 25 ηspdc(ppln) mm-long VS cm-long vaveguides ħωp 06/22

II/ AlGaAs source SPDC, different phase-matching techniques energy conservation: ωa + ωb = ωp (with ωa ωb) Δ[ħω] = 0 phase-matching (momentum conservation): Δ[ħk] = Δ[ħnω/c] = 0 n(ωa)ωa + n(ωb)ωb = n(ωp)ωp n(½ωp) = n(ωp) n 0 ½ωp ωp ω 07/22

II/ AlGaAs source SPDC, different phase-matching techniques 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) z ΛQPM 08/22

II/ AlGaAs source SPDC, different phase-matching techniques 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) z ΛQPM birefringent PM: nte(½ωp) = ntm(ωp) insertion of Al-Oxyde layers (fragile material) TE n z TM 0 TE TM ½ωp ωp ω 08/22

II/ AlGaAs source SPDC, modal phase-matching technique energy conservation: ωa + ωb = ωp (with ωa ωb) phase-matching (modal, type II): nte00(ωa)ωa + ntm00(ωb)ωb = ntebragg(ωp)ωp ntm00(ωa)ωa + nte00(ωb)ωb = ntebragg(ωp)ωp n TE00 TM00 TEBragg (1) (2) transverse modes: TEBragg TE00 TM V TE H z 0 ωa ωb ½ωp ωp TM00 ω F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014). C. Autebert et al., Optica 3, 143-146 (2016). core layer Bragg mirrors 09/22

II/ AlGaAs source 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 transverse modes: TEBragg TE00 TM00 F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014). 10/22

II/ AlGaAs source Direct polarization Bell state generation over a large bandwidth ωp TE00 TM00 TE00 30 nm H,ωA V,ωB TM00 λp (nm) ωp or λa,b (nm) λa,b (nm) λa,b (nm) 8 nm 6. 8 7 7 λp = intensity (a.u.) ΨA,B = V,ωA H,ωB HV + eiφ VH 2 very small birefringence no need for walk-off compensation nor interferometric schemes F. Boitier et al., Phys. Rev. Lett. 112, 183901 (2014). 11/22

III/ Ressource optimisation DWDM Dense Wavelength Division Multiplexing (DWDM) 0.8 nm (100 GHz) 73 laser diodes 1 long-distance SMF fiber 73 channels DEMUX MUX Internet server ITU 100 GHz grid 01 1577.03 nm 02 1576.20 nm 03 1575.37 nm 71 1521.02 nm 72 1520.25 nm 73 1519.48 nm 73 homes neighbourhood Internet access a single fiber deployed for many users 12/22

III/ Multi-user entanglement distribution Dense Wavelength Division Multiplexing (DWDM) 0.8 nm (100 GHz) 1 entanglement source 36 channel pairs Ψ DEMUX quantum Internet server ITU 100 GHz grid 01 1577.03 nm 02 1576.20 nm 03 1575.37 nm 71 1521.02 nm 72 1520.25 nm 73 1519.48 nm Bob 3 Bob 2 Bob 1 Alice 1 Alice 2 Alice 3 72 clients 36 pairs of clients 72 SMF fibers distribution of entangled photon pairs between symmetric channels around the degeneracy wavelength a single source for many pairs of users J. Trapateau et al., J. Appl. Phys. 118, 143106 (2015). 13/22

III/ Multi-user entanglement distribution 08 1571.24 nm 25 1557.36 nm 42 1543.73 nm DWDM & large-band frequency anti-correlation λp = 778.68 nm ωb TE00 JSI(A,B) (narrow-linewidth pumping) ωb = ωp ωa TM00 λa 42 30 nm 15 nm 25 λb intensity (a.u.) 25 15 nm 08 25 ωa 16 pairs of channels/users available over the 30-nm bandwidth of the entangled pairs 14/22

III/ Multi-user entanglement distribution DWDM & large-band frequency anti-correlation ωb JSI(A,B) (narrow-linewidth pumping) ITU 100 GHz grid: 21 1560.61 nm 22 1559.79 nm 23 1558.98 nm 24 1558.17 nm 25 1557.36 nm 26 1556.55 nm 27 1555.75 nm 28 1554.94 nm 29 1554.13 nm ωb = ωp ωa 29 28 27 26 25 21 22 23 24 25 ωa 4 pairs of channels/users in our experiment (8+1 channels DWDM) 15/22

IV/ Multi-user BBM92-QKD experiment quantum server AlGaAs waveguide holographic mask 63x B29 B28 DWDM B26 A24 10x SMF collimator CW Ti:sa laser Peltier cooler 778.68 nm A22 A21 long-pass filter fiber links Alice 23 polarization controller Bob 27 APD time coincidence counter APD λ/2 PBS polarization controller PBS λ/2 16/22

IV/ Multi-user BBM92-QKD experiment BBM92 protocol: H/V H/V quantum server HV VH Ψ AB = = 2 + + t1 2 +/ t2 Ψ AB t3 t1 t2 t3 +/ ❶ local basis choices & coincidence measurements Rraw ❷ basis reconcilliation (sifting) Rsift = ½Rraw t1 ❶ t2 t3 t4 t5 t6 t7 t8 AB AB AB AB AB AB AB AB 10 +0 00 + 1 + 0+ +1 ❷ 10 00 01 10 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). 17/22

IV/ Multi-user BBM92-QKD experiment BBM92 protocol: H/V H/V quantum server HV VH Ψ AB = = 2 + + 2 t1 +/ t2 Ψ AB t3 t1 t2 t3 +/ 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) t1 ❶ t2 t3 t4 t5 t6 t7 t8 AB AB AB AB AB AB AB AB 10 +0 00 + 1 + 0+ +1 ❷ 10 00 01 10 ❸ 10 01 01 10 ❹ 0 1 0 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). 17/22

IV/ Multi-user BBM92-QKD experiment Coincidence histograms for A23 B27 over 50 km: Cfalse Rsift = Cmin Cmax + Cmin τhisto Cfalse Rfalse = Cmax Cfalse τhisto V= Cmax Cmin Cmax + Cmin e = ½(1 V) E. Waks, A. Zeevi & Y. Yamamoto, Phys. Rev. A 65, 052310 (2002). 18/22

IV/ Multi-user BBM92-QKD experiment 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% 19/22

IV/ 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% 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% 20/22

V/ 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 21/22

question time arxiv:1607.01693 22/22