Experimental demonstration of continuous variable quantum key distribution over 80 km of standard telecom fiber

Why is QKD not used?Towards high-performance CVQKD

Practical security considerations

Experimental Demonstration ofContinuous-Variable Quantum Key Distribution

over 80 km of Standard Telecom Fiber

Paul Jouguet, Sebastien Kunz-Jacques, AnthonyLeverrier, Philippe Grangier, Eleni Diamanti

SeQureNet, Telecom ParisTech

2012-09-14

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QKD: four main limitations (1/2)

Speed

I Not enough for OTP: not a serious issue

I Physical parameters estimation over large blocks: hardwaredrifts, latency

Distance

I Asymmetric crypto is not limited

I Trusted nodes are not a good solution: quantum repeaters arerequired

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QKD: four main limitations (2/2)

Security

I Incomplete security proofs

I Distance between proofs and practical implementations

Deployment

I QKD requires a dark fiber: $$$

I WDM compatibility: lowers QKD extra premium

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Two technologies

Discrete variables Continuous variables

medium photon phase/polar. field amplitude-phasedetection photon counters coherent detection

range 100 km 25kmrate 1Mb/s 10kb/s

components active cooling standardintegration WDM WDM

security yes yes

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Gaussian protocol

Losses and excess noise lower the SNR.

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Optical setup

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Speed limitations

I Delay between classical and quantum signals (200ns)

I Laser pulsed with a tunable frequency (1MHz)

I Data acquisition speed (up to 5MHz)

I Filtering: tradeoff between speed and electronic noise (currentcutoff at 10MHz, 100MHz feasible arxiv:1006.1257 Yue-MengChi et al.)

I High-speed error correction: LDPC codes (GPU) or polarcodes (CPU) (up to 10Mbit/s) (arxiv:1204.5882, P. Jouguetand S. Kunz-Jacques)

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Range limitations

I High error-correction efficiency, even at low SNRs

I Finite-size effects

I Low SNR Alice/Bob synchronization mechanism

I Low-loss LO path

I Excess noise (imperfect relative phase estimation)

New SNR regions allowed by error-correction techniques.

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Channel virtualization

I Idea introduced by Leverrier (Phys. Rev. A 77, 042325(2008))

I Translates the initial problem into a channel coding problemon a good channel

I Good means very efficient error-correcting codes available

I Usual suspect: BIAWGNC

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How to improve the efficiency of the multidimensionalscheme?

I Improve the approximation between the virtual channel andthe target channel

I Improve the efficiency of the codes on the target channel(Phys. Rev. A 84, 062317 (2011), P. Jouguet, S.Kunz-Jacques and A. Leverrier)

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What is a good code for the BIAWGNC?

I A code is designed for a channel and a SNR

I Free parameter: the code rate R = n−mn , m the number of

parity-check equations, n the length

I Low SNR / Lot of redundancy / Low rate

I Efficiency β (SNR) = RC(SNR)

I Typical values:I Slice reconciliation: β = 90%, SNR= 3, @30kmI Multidimensional reconciliation: β = 89%, SNR= 0.5, @50km

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Set of available codes

β SNR

93.6% 1.09793.1% 0.16195.8% 0.07596.9% 0.02996.6% 0.014595.9% 0.00725

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How to get more flexibility on the SNR?

I Possible to design codes with lower rates

I Not necessary: repetition codes

I Shortening, puncturing

I Optimization on the modulation variance

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Theoretical secret key rate

Parameters: VA ∈ {1, 100}, T = 10−0.2d/10, ξ = 0.01, η = 0.6,Velec = 0.01

10−6

10−5

0.0001

0.001

0.01

0.1

1

0 20 40 60 80 100 120 140 160 180

Key

rate

(secretbits/pulse)

Distance (km)

1SNR=1.097 (1)

2

SNR=0.161 (2)

3

SNR=0.075 (3)

4

SNR=0.029 (4)

5

SNR=0.0145 (5)

6

SNR=0.00725 (6)

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Finite size effects

I First analysis for discrete modulation protocols in Phys. Rev.A 81, 062343 (2010), Leverrier et al.

I Statistical uncertainty over estimated parameters (T , ξ)

I K = nN (βI (x ; y)− SεPE (y ;E )−∆(n))

I Extended analysis for Gaussian modulation, includingimperfect homodyne detection (efficiency, electronic noise)and shot noise estimation (Phys. Rev. A 86, 032309 (2012),poster 33)

I Main effect: uncertainty on the excess noise ξ

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Experimental results

Parameters: d = 53km, η = 0.552, Velec = 0.015, SNR= 0.17,β = 94%, ε = 10−10

-0.0005

0

0.0005

0.001

0.0015

0.002

0 5 10 15 20

Excess

noise(shotnoiseunits)

Time (hours)

excess noisestd dev of the experimental excess noise

std dev of the theoretical estimator (108 samples)std dev of the theoretical estimator (106 samples)

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Experimental results

Parameters: d = 53km,80km, η = 0.552, Velec = 0.015,SNR=0.17,0.08, β = 94%, ε = 10−10

100

1000

10000

100000

0 20 40 60 80 100

Key

rate

(bit/s)

Distance (km)

asymptotic theoretical key rate�nite-size theoretical key rate (108 samples)

asymptotic experimental point�nite-size experimental point (108 samples)

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Imperfect preparation

I Thermal noise (Phys. Rev. A 81, 022318 (2010), Usenko andFilip)

I Gaussian modulation: truncated and discretized (finiteamount of randomness)

I Can be taken into account into the security proof (Phys. Rev.A 86, 032309 (2012), poster 33)

I But a lot of random numbers are required (+ sifting andmultidimensional protocol)

I Calibration proceduresI Calibration of the homodyne detectionI Calibration of the phase noise

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Summary

I Long distance CVQKD with Gaussian modulation is possiblethanks to low SNR error-correction capability

I Computing-power consuming because of decoding close to thethreshold

I We use GPU (30× faster than CPU plus friendly Moore’s law)

I Higher secure distance with virtual Gaussian post-selection?(arxiv:1205.6933, J. Fiurasek, N. J. Cerf, arxiv:1206.0936, N.Walk et al.)

I Work on WDM coming

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Enquire about Cygnus

I An open and customizable CVQKD research platform

I Tests/demonstrations of integration in optical networks

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Technology

Experimental demonstration of continuous variable quantum key distribution over 80 km of standard telecom fiber