High rate quantum cryptography with untrusted relay: Theory and experiment

Transcription

1 High rate quantum cryptography with untrusted relay: Theory and experiment CARLO OTTAVIANI Department of Computer Science, The University of York (UK) 1st TWQI Conference Ann Arbor 27-3 July

2 In collaboration with: Stefano Pirandola Sam Braunstein Gaetana Spedalieri Seth Lloyd Christian Weedbrook Tobias Gehring Christian S. Jacobsen Ulrik L. Andersen Nature Photonics 9, , (2015)

3 Outline Measurement-device independence (MDI) Protocol with continuous variables (CVs) Reduction of the general attack Secret-key rate and security distances Symmetric configuration Optimal configuration Experimental results Conclusions and outlook

4 Measurement-device independence Alice Private space Random states Relay (Eve) Measurement Public channel Random states Bob Private space Braunstein & Pirandola PRL 108, (2012) Arbitrary systems & measurements (quantum instruments) Lo, Curty & Qi PRL 108, (2012) Qubit regime (decoy states, Bell detection) 4

5 Continuous Variables Next step: MDI quantum cryptography with Continuous Variables Why? Cheap quantum sources (amplitude-modulated coherent states) Efficient homodyne detectors which can also go broadband High rates compared to discrete variables (qubits) Weedbrook, Pirandola, et al. Rev. Mod. Phys. 84, (2012) 5

6 Working mechanism with CVs γ q- p + γ := q + ip + 2 Alice α A Bell Relay B Bob β Two main ingredients: Gaussian-modulated coherent states CV Bell detection (balanced beamsplitter + homodynes) S. Pirandola et al., Nature Photonics 9, , (2015) 6

7 Working mechanism with CVs Relay creates correlations γ q- p + Alice α A Bell Relay B Bob β γ = α β + noise Processing Alice and Bob share information Eve cannot eavesdrop from : γ I(α,β γ ) > 0 I(α γ) = I(β γ ) = 0 7

8 Alice α A General Attack: Joint on links and relay Eve cannot eavesdrop from γ : I(α γ) = I(β γ ) = 0 Simulator γ U QM (we bound Eve with the Holevo information which is unitarily invariant, so that we can play with U) E p(α,β,γ) B Bob β For a given observed statistics Alice and Bob can assume that: Simulator = Bell detection 8

9 Reduction of the joint attack: Coherent Gaussian attack Bell relay γ Alice α A U QM E B Bob β Coherent attack of the links Gaussian protocol U Gaussian unitary (Coherent Gaussian attack) 9

10 Coherent Gaussian attack Bell relay γ QM τ A τ B QM Alice α A E 1 E 2 B Bob β Realistic attack V E1,E 1 = ω AI G G = g G ω B I g ʹ 10

11 Security Analysis entanglement-based representation Bell relay γ QM τ A τ B QM α Alice a ρ A α E 1 E 2 B β Bob ρ b β Since local detections commute, we can consider the conditional states after the Bell detection of the relay Post relay Alice α a ρ ab γ b β Bob 11

12 Alice and Bob s mutual information I(α : β) = log 2 µ Security Analysis Variance of modulation µ >>1 χ Equivalent noise χ = χ +ε L R = ξi(α : β) I(α : E) Eve s Holevo information Alice α a ΦabE γ ρ ab γ E ρ b E γ β Bob 12

13 Secret-key rate R(τ A,τ B,χ) = log 2 2(τ A +τ B ) e τ A τ B χ + h(x) h(y) x = τ Aχ 1 y = τ Aτ B χ (τ A +τ B ) τ A +τ τ B A τ B τ A +τ B 2 ξ =1 Function of the transmissivities and the equivalent noise h(x) = x +1 2 log 2 x +1 2 x 1 2 log 2 x 1 2 S. Pirandola et al., Nature Photonics 9, , (2015) 13

14 Symmetric Configuration Relay γ Alice a α A QM A B E 1 E 2 e τ E 1 E 2 QM ω A = ω B = ω τ A = τ B = τ τ QM β B b Bob τ 2 R = log 2 λλ'(τ + λ)(τ + λ') + h λ = (1 τ)(ω g) + 1 η η (τ + 2λ)(τ + 2λ') τ λ = (1 τ)(ω + g ʹ ) + 1 η ʹ η ʹ CO, G.spedalieri, S.L. Braunstein, S. Pirandola, PRA 91, (2015) 14

15 Joint symmetric attacks Collective Attacks: (1) g ʹ = g = 0 Separable Attacks: (2),(3),(4) EPR Attacks: g ʹ = g = ±(ω 1) (5),(6) g ʹ = g = ± ω 2 1 (6) is optimal! CO, G.spedalieri, S.L. Braunstein, S. Pirandola, PRA 91, (2015) 15

16 Security thresholds EPR attack, (6), is optimal! CO et al., PRA 91, (2015) 16

17 Maximum Performance: pure loss τ R(τ A,τ B ) = log A τ B 2 + h 2 1 h 2 τ τ A B e τ A τ B τ B τ A τ B Alice radius r Relay A distance d, Bob 0.2dB/km (fiber) S. Pirandola et al., Nature Photonics 9, , (2015) See also Preprint arxiv:

18 Robustness to excess noise χ = χ L + ε ε = 0 ε = 0.1 Nature Photonics 9, , (2015) 18

19 Experimental Setup (Christian S. Jacobsen, Tobias Gehring, Ulrik L. Andersen) Nature Photonics 9, , (2015). see also arxiv:

20 Experimental Results Parameters: Excess noise 0.01; ϕ = 60 SNU ξ = 1 ξ = 0.97 ξ = 0.95 (a) Bob distance 25 Km; Rate 10-2 (b) Alice at 100 mt Bob at Km; Rate 10-2 (c) Alice at 1 Km; Bob at Km; Rate 10-2 Nature Photonics, 9, , (2015) 20

21 Few points on CV experiments I Cheap room temperature components (optical modulators ad homodyne detections) Regime of parameters easily achievable in practice Gaussian modulation ~ 60 shot noise units (easy) CV Bell detection efficiency routinely high (η ~ 98%) and can be done in free space Reconciliation efficiency ξ ~ 97% state-of-the-art Excess-noise in our experiment is ε ~0.01 arxiv: for more visit Stefano s Poster

22 Few points on CV experiments II Our experimental rate is a lower bound The theoretical rate is optimal Finite-size effects and composable security support our experimental results The relay doesn t need to be in Alice s Lab Interfering signals from independent laser sources is no longer a security issue or major experimental challenge in CV-QKD Fast time-resolved homodyne detectors are available with bandwidths of 100MHz and more arxiv: for more visit Stefano s Poster

23 A comparison CVs-DVs arxiv: for more visit Stefano s Poster

24 Typical network topology Mobile device connecting to a public access point 24

25 Conclusions A conceptual advance Untrusted relays versus the trusted relays used in the current network prototypes (SECOQC, Tokyo network ) Our untrusted relay performs cheap operations with all the complexity left to the end-users First steps towards the realization of the end-to-end principle in a quantum network over metropolitan distances Outlook: More complex structures with less trusted nodes Extension to thermal-qkd: to use different frequencies for mixed technology platforms (microwave/infrared) 25

26 Thx for your attention