Introduction. Slice reconciliation. High bit rate CVQKD. Summary. Quantum Key Distribution. Quantum Channel. IAB. IAE. I
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
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Introduction
Slice reconciliation
High bit rate CVQKD
Summary
Quantum Key Distribution
Quantum Channel
Exchange of quantum states
arXiv:1406.1050
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Introduction
Slice reconciliation
High bit rate CVQKD
Summary
Quantum Key Distribution IBE
IAE Quantum Channel
IAB Exchange of quantum states Induced correlations
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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
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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 }
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
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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 ). information revealed during reconciliation
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 ). information revealed during reconciliation K = βIAB − min{IAE , IBE }
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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 ). information revealed during reconciliation K = βIAB − min{IAE , IBE } with β < 1. arXiv:1406.1050
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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) 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
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1
10 SNR
100
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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 y1 , . . . , yn
Bob
Each slice of the m-bit source is independently encoded
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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
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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 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
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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
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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
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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
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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
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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
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
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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
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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
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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
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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
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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
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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
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Introduction
Slice reconciliation
High bit rate CVQKD
Summary
Summary β > 0.93 for all practical SNRs
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)
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
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