On the problem of non-zero word error rates for fixed-rate error correction codes in continuous variable quantum key distribution

Johnson, Sarah J.; Lance, Andrew M.; Ong, Lawrence; Shirvanimoghaddam, Mahyar; Ralph, T. C.; Symul, Thomas

doi:10.1088/1367-2630/aa54d7

Cited by 8 publications

(2 citation statements)

References 30 publications

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“…In the remainder of this review, we will restrict our analysis to the case of reverse reconciliation. Equation is valid for an ideal system; however, if we take into account that information reconciliation does not operate at the (asymptotic) Shannon limit, that a fraction of blocks (frames) will fail to reconcile, and that a fraction of the symbols is used for error estimation we obtain the asymptotic secure‐key fraction of a practical CV‐QKD system:

\begin{matrix} true \\ right r_{coll}^{asympt} \geq (1 - FER) (1 - ν) (β I_{A B} - χ_{E B}) \end{matrix}

Here,

FER \in [0, 1]

and

β \in [0, 1]

represent the frame‐error rate and the efficiency of information reconciliation, respectively, and

ν \in [0, 1]

is the fraction of the symbols which has to be disclosed in order to estimate the entries of the covariance matrix. The efficiency β measures how closely an information reconciliation method approaches the theoretical limit.…”

Section: Notions Of Security and Secure‐key Ratementioning

confidence: 99%

Continuous‐Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations

et al. 2018

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Quantum key distribution (QKD) using weak coherent states and homodyne detection is a promising candidate for practical quantum‐cryptographic implementations due to its compatibility with existing telecom equipment and high detection efficiencies. However, despite the actual simplicity of the protocol, the security analysis of this method is rather involved compared to discrete‐variable QKD. This article reviews the theoretical foundations of continuous‐variable quantum key distribution (CV‐QKD) with Gaussian modulation and rederives the essential relations from scratch in a pedagogical way. The aim of this paper is to be as comprehensive and self‐contained as possible in order to be well intelligible even for readers with little pre‐knowledge on the subject. Although the present article is a theoretical discussion of CV‐QKD, its focus lies on practical implementations, taking into account various kinds of hardware imperfections and suggesting practical methods to perform the security analysis subsequent to the key exchange. Apart from a review of well‐known results, this manuscript presents a set of new original noise models which are helpful to get an estimate of how well a given set of hardware will perform in practice.

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\begin{matrix} true \\ right r_{coll}^{asympt} \geq (1 - FER) (1 - ν) (β I_{A B} - χ_{E B}) \end{matrix}

Here,

FER \in [0, 1]

and

β \in [0, 1]

represent the frame‐error rate and the efficiency of information reconciliation, respectively, and

ν \in [0, 1]

Section: Notions Of Security and Secure‐key Ratementioning

confidence: 99%

Continuous‐Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations

et al. 2018

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“…The unavoidable high level of channel excess noise is common in practical application of the CVQKD protocol [33], and its fluctuation will further lower the reconciliation efficiency. Moreover, a recent report [34] shows that the frame error rate [28,35,36] of the ECC may further restrict the real reconciliation efficiency.…”

Section: Introductionmentioning

confidence: 99%

Quantum key distribution using basis encoding of Gaussian-modulated coherent states

Huang

Zhang

et al. 2018

Phys. Rev. A

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The continuous-variable quantum key distribution (CVQKD) has been demonstrated to be available in practical secure quantum cryptography. However, its performance is restricted strongly by the channel excess noise and the reconciliation efficiency. In this paper, we present a quantum key distribution (QKD) protocol by encoding the secret keys on the random choices of two measurement bases: the conjugate quadratures X and P. The employed encoding method can dramatically weaken the effects of channel excess noise and reconciliation efficiency on the performance of the QKD protocol. Subsequently, the proposed scheme exhibits the capability to tolerate much higher excess noise and enables us to reach a much longer secure transmission distance even at lower reconciliation efficiency. The proposal can work alternatively to strengthen significantly the performance of the known Gaussian-modulated CVQKD protocol and serve as a multiplier for practical secure quantum cryptography with continuous variables.

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Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems

Jeong

Jung

2022

npj Quantum Inf

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In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.

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On the problem of non-zero word error rates for fixed-rate error correction codes in continuous variable quantum key distribution

Cited by 8 publications

References 30 publications

Continuous‐Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations

Continuous‐Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations

Quantum key distribution using basis encoding of Gaussian-modulated coherent states

Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems

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