Introduction

Slice reconciliation

High bit rate CVQKD

Summary

High Bit Rate Continuous-Variable Quantum Key Distribution Paul Jouguet, David Elkouss, S´ebastien Kunz-Jacques arXiv:1406.1050

Slide 1/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantum Key Distribution

Quantum Channel

Exchange of quantum states

arXiv:1406.1050

Slide 2/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantum Key Distribution IBE

IAE Quantum Channel

IAB Exchange of quantum states Induced correlations

arXiv:1406.1050

Slide 2/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantum Key Distribution IBE

IAE Public Classical Channel Quantum Channel

IAB Exchange of quantum states Induced correlations Public discussion: reconciliation + privacy amplification arXiv:1406.1050

Slide 2/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE }

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE } Practice: Distillable key depends on:

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE } Practice: Distillable key depends on: estimate on IAE (IBE ).

arXiv:1406.1050

Slide 3/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE } Practice: Distillable key depends on: estimate on IAE (IBE ). information revealed during reconciliation

arXiv:1406.1050

Slide 3/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE } Practice: Distillable key depends on: estimate on IAE (IBE ). information revealed during reconciliation K = βIAB − min{IAE , IBE }

arXiv:1406.1050

Slide 3/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Secret Key Rate Theory: For any tripartite state ρABE Devetak-Winter formula: K = IAB − min{IAE , IBE } Practice: Distillable key depends on: estimate on IAE (IBE ). information revealed during reconciliation K = βIAB − min{IAE , IBE } with β < 1. arXiv:1406.1050

Slide 3/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE }

arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1

arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1 Gaussian protocol CVQKD

arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1 Gaussian protocol CVQKD Induced Gaussian channel: IAB = 12 log(1 + SNR). Potentially K > 1,

arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1 Gaussian protocol CVQKD Induced Gaussian channel: IAB = 12 log(1 + SNR). Potentially K > 1, if we have good codes

arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1 Gaussian protocol CVQKD Induced Gaussian channel: IAB = 12 log(1 + SNR). Potentially K > 1, if we have good codes Goal: good reconciliation efficiency for low and medium distances. Optimize slice reconciliation. arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

The promise of CVQKD DVQKD Most protocols use binary variables IAB − min{IAE , IBE } 6 IAB 6 H(A) 6 1 Gaussian protocol CVQKD Induced Gaussian channel: IAB = 12 log(1 + SNR). Potentially K > 1, if we have good codes Goal: good reconciliation efficiency for low and medium distances. Optimize slice reconciliation. Gehring et al, arXiv:1406.6174 arXiv:1406.1050

Slide 4/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Slice reconciliation

Proposed by G. Van Assche, J. Cardinal, and N. J. Cerf, IEEE TIT, 2004.

arXiv:1406.1050

Slide 5/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Slice reconciliation

Proposed by G. Van Assche, J. Cardinal, and N. J. Cerf, IEEE TIT, 2004. Reconciliation method for non-binary sources

arXiv:1406.1050

Slide 5/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Slice reconciliation

Proposed by G. Van Assche, J. Cardinal, and N. J. Cerf, IEEE TIT, 2004. Reconciliation method for non-binary sources Binary source codes

arXiv:1406.1050

Slide 5/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Slice reconciliation

Proposed by G. Van Assche, J. Cardinal, and N. J. Cerf, IEEE TIT, 2004. Reconciliation method for non-binary sources Binary source codes Two steps: quantization and encoding

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantization m qm 1 , . . . , qn

x1 , . . . , xn

Q

q21 , . . . , q2n q11 , . . . , q1n

Alice

Choose a quantizer Q : R → {0, 1}m

arXiv:1406.1050

Slide 6/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantization Uniform

m qm 1 , . . . , qn

x1 , . . . , xn

Q

−∞ q21 , . . . , q2n

0



q11 , . . . , q1n

Alice

Non-uniform

Choose a quantizer Q : R → {0, 1}m Constant vs optimized steps

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantization Uniform

m qm 1 , . . . , qn

x1 , . . . , xn

Q

−∞ q21 , . . . , q2n

0



q11 , . . . , q1n

Alice

Non-uniform

Choose a quantizer Q : R → {0, 1}m Constant vs optimized steps I(X; Y) > I(Q(X); Y) arXiv:1406.1050

Slide 6/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantization Uniform

m qm 1 , . . . , qn

x1 , . . . , xn

Q

−∞ q21 , . . . , q2n

0



q11 , . . . , q1n

Alice

Non-uniform

Choose a quantizer Q : R → {0, 1}m Constant vs optimized steps I(X; Y) > I(Q(X); Y) Increase the number of slices arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Quantization optimization uniform m=3 non-uniform m=3

uniform m=4 non-uniform m=4

uniform m=5 non-uniform m=5

100

I(Q(X);Y)/I(X;Y) (%)

95 90 85 80 75 70

arXiv:1406.1050

1

10 SNR

100

Slide 7/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Source Coding m qm 1 , . . . , qn

x1 , . . . , xn

Q

q21 , . . . , q2n

ENCm ENC2

m sm 1 , . . . , sn(1−Rm )

s21 , . . . , s2n(1−R ) 2

DECm DEC2

q11 , . . . , q1n

m qˆ m 1 , . . . , qˆ n

qˆ 21 , . . . , qˆ 2n qˆ 11 , . . . , qˆ 1n

Alice y1 , . . . , yn

Bob

Each slice of the m-bit source is independently encoded

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Source Coding m qm 1 , . . . , qn

x1 , . . . , xn

Q

q21 , . . . , q2n

ENCm ENC2

m sm 1 , . . . , sn(1−Rm )

s21 , . . . , s2n(1−R ) 2

DECm DEC2

q11 , . . . , q1n

m qˆ m 1 , . . . , qˆ n

qˆ 21 , . . . , qˆ 2n qˆ 11 , . . . , qˆ 1n

Alice Bob

y1 , . . . , yn

Each slice of the m-bit source is independently encoded A different binary code of the appropriate rate is used for each layer arXiv:1406.1050

Slide 8/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Source Coding m qm 1 , . . . , qn

x1 , . . . , xn

Q

q21 , . . . , q2n

ENCm ENC2

m sm 1 , . . . , sn(1−Rm )

s21 , . . . , s2n(1−R ) 2

DECm DEC2

q11 , . . . , q1n

m qˆ m 1 , . . . , qˆ n

qˆ 21 , . . . , qˆ 2n qˆ 11 , . . . , qˆ 1n

Alice Bob

y1 , . . . , yn

Each slice of the m-bit source is independently encoded A different binary code of the appropriate rate is used for each layer Very noisy slices are transmitted unencoded arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Effect of imperfect codes on reconciliation efficiency Perfect codes βdisc

arXiv:1406.1050

H(Q(X)) − m + = I(X; Y)

Pm

i=1 Ci

Slide 9/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Effect of imperfect codes on reconciliation efficiency Perfect codes βdisc

H(Q(X)) − m + = I(X; Y)

Pm

i=1 Ci

Ri < Ci :

P H(Q(X)) − m + m i=1 βci Ri β= I(X; Y)

with βci = Ri /Ci

arXiv:1406.1050

Slide 9/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Effect of imperfect codes on reconciliation efficiency Perfect codes βdisc

H(Q(X)) − m + = I(X; Y)

Pm

i=1 Ci

Ri < Ci :

P H(Q(X)) − m + m i=1 βci Ri β= I(X; Y)

with βci = Ri /Ci Equilibrium between number of slices m and βc arXiv:1406.1050

Slide 9/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Slice number optimization m=3

m=4

m=5

1

0.95

β

0.9

0.85

0.8

0.75

0.7 1

10 SNR

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Reconciliation Efficiency

Good efficiencies in the SNR range [1, 60]

arXiv:1406.1050

SNR Efficiency 0.55 93.4% 93.7% 0.86 1 94.2% 3 94.1% 5.12 94.4% 14.57 95.8% 94.8% 66.10

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Reconciliation Efficiency

Good efficiencies in the SNR range [1, 60] New LDPC codes with βc > 0.95

arXiv:1406.1050

SNR Efficiency 0.55 93.4% 93.7% 0.86 1 94.2% 3 94.1% 5.12 94.4% 14.57 95.8% 94.8% 66.10

Slide 11/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Reconciliation Efficiency

Good efficiencies in the SNR range [1, 60] New LDPC codes with βc > 0.95 Constant step

arXiv:1406.1050

SNR Efficiency 0.55 93.4% 93.7% 0.86 1 94.2% 3 94.1% 5.12 94.4% 14.57 95.8% 94.8% 66.10

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Reconciliation Efficiency

Good efficiencies in the SNR range [1, 60] New LDPC codes with βc > 0.95 Constant step 3/5 Slices

arXiv:1406.1050

SNR Efficiency 0.55 93.4% 93.7% 0.86 1 94.2% 3 94.1% 5.12 94.4% 14.57 95.8% 94.8% 66.10

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Reconciliation Efficiency

Good efficiencies in the SNR range [1, 60] New LDPC codes with βc > 0.95 Constant step 3/5 Slices For SNR< 1 (Jouguet et al, NP 2013) arXiv:1406.1050

SNR Efficiency 0.0075 95.9% 96.6% 0.0145 0.029 96.9% 0.075 95.8% 0.161 93.1% 1.097 93.6%

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Application to state of the art CVQKD Coherent states with homodyne measurement

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Application to state of the art CVQKD Coherent states with homodyne measurement Asymptotic key rate / collective attacks

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Application to state of the art CVQKD Coherent states with homodyne measurement Asymptotic key rate / collective attacks ξ = 0.0015VA , α = 0.2, η = 0.6, velec = 0.01, sifting = 10%, clock = 1MHz arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

Distance 0.1 35 50 65 70

High bit rate CVQKD

Summary

1 MHz 1.04 × 106 1.4 × 104 5.4 × 103 2.5 × 103 1.9 × 103

Application to state of the art CVQKD Coherent states with homodyne measurement Asymptotic key rate / collective attacks ξ = 0.0015VA , α = 0.2, η = 0.6, velec = 0.01, sifting = 10%, clock = 1MHz arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

Distance 0.1 35 50 65 70

1 MHz 1.04 × 106 1.4 × 104 5.4 × 103 2.5 × 103 1.9 × 103

High bit rate CVQKD

Summary

50 MHz 5.2 × 107 6.8 × 105 2.7 × 105 1.2 × 105 9.6 × 104

Application to state of the art CVQKD Coherent states with homodyne measurement Asymptotic key rate / collective attacks ξ = 0.0015VA , α = 0.2, η = 0.6, velec = 0.01, sifting = 10% arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

Distance 0.1 35 50 65 70

1 MHz 1.04 × 106 1.4 × 104 5.4 × 103 2.5 × 103 1.9 × 103

High bit rate CVQKD

50 MHz 5.2 × 107 6.8 × 105 2.7 × 105 1.2 × 105 9.6 × 104

Summary

DVQKD (1 GHz) 2.4 × 106 1.2 × 106 1.8 × 105 5.2 × 104

Comparison with DVQKD Experiment with highest throughput (Patel et al, APL 2014.)

arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

Distance 0.1 35 50 65 70

1 MHz 1.04 × 106 1.4 × 104 5.4 × 103 2.5 × 103 1.9 × 103

High bit rate CVQKD

50 MHz 5.2 × 107 6.8 × 105 2.7 × 105 1.2 × 105 9.6 × 104

Summary

DVQKD (1 GHz) 2.4 × 106 1.2 × 106 1.8 × 105 5.2 × 104

Comparison with DVQKD Experiment with highest throughput (Patel et al, APL 2014.) Multiplexed signals

arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

Distance 0.1 35 50 65 70

1 MHz 1.04 × 106 1.4 × 104 5.4 × 103 2.5 × 103 1.9 × 103

High bit rate CVQKD

50 MHz 5.2 × 107 6.8 × 105 2.7 × 105 1.2 × 105 9.6 × 104

Summary

DVQKD (1 GHz) 2.4 × 106 1.2 × 106 1.8 × 105 5.2 × 104

Comparison with DVQKD Experiment with highest throughput (Patel et al, APL 2014.) Multiplexed signals Comparable throughput arXiv:1406.1050

Slide 12/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Summary β > 0.93 for all practical SNRs

arXiv:1406.1050

Slide 13/13

Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Summary β > 0.93 for all practical SNRs Applied to state of the art CVQKD (1 MHz)

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Summary β > 0.93 for all practical SNRs Applied to state of the art CVQKD (1 MHz) d < 100 m, more than 1 bit per symbol can be distilled

arXiv:1406.1050

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Introduction

Slice reconciliation

High bit rate CVQKD

Summary

Summary β > 0.93 for all practical SNRs Applied to state of the art CVQKD (1 MHz) d < 100 m, more than 1 bit per symbol can be distilled Projections for improved clock rate (50 MHz) would render throughputs comparable to DVQKD

arXiv:1406.1050

Slide 13/13

High Bit Rate Continuous-Variable Quantum Key ...

Introduction. Slice reconciliation. High bit rate CVQKD. Summary. Quantum Key Distribution. Quantum Channel. IAB. IAE. IBE. Exchange of quantum states. Induced correlations. arXiv:1406.1050. Slide 2/13 ...

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