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arXiv:quant-ph/0511207 · Physical Review A

Cloning and optimal Gaussian individual attacks for a continuous-variable quantum key distribution using coherent states and reverse reconciliation

Ryo Namiki, Masato Koashi, Nobuyuki Imoto

Published Mar 2, 2006• 10 citations
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Abstract

We investigate the security of continuous-variable quantum key distribution using coherent states and reverse reconciliation against Gaussian individual attacks based on an optimal Gaussian $1\ensuremath{\rightarrow}2$ cloning machine. We provide an implementation of the optimal Gaussian individual attack. We also find a Bell-measurement attack which works without delayed choice of measurements and has better performance than the cloning attack.

DOI
10.1103/physreva.73.032302

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We investigate the security of continuous-variable quantum key distribution using coherent states and reverse reconciliation against Gaussian individual attacks based on an optimal Gaussian 1\ensuremath→21\ensuremath{\rightarrow}21\ensuremath→2 cloning machine. We provide an implementation of the optimal Gaussian individual attack. We also find a Bell-measurement attack which works without delayed choice of measurements and has better performance than the cloning attack.
We analyze a reversibility of optimal Gaussian $\stackrel{\ensuremath{\rightarrow}}{1}2$ quantum cloning of a coherent state using only local operations on the clones and classical communication between them and propose a feasible experimental test of this feature. Performing Bell-type homodyne measurement on one clone and anticlone, an arbitrary unknown input state (not only a coherent state) can be restored in the other clone by applying appropriate local unitary displacement operation. We generalize this concept to a partial reversal of the cloning using only local operations and classical communication (LOCC) and we show that this procedure converts the symmetric cloner to an asymmetric cloner. Further, we discuss a distributed LOCC reversal in optimal $\stackrel{\ensuremath{\rightarrow}}{1}M$ Gaussian cloning of coherent states which transforms it to optimal $\stackrel{\ensuremath{\rightarrow}}{1}{M}^{\ensuremath{'}}$ cloning for ${M}^{\ensuremath{'}}<M.$ Assuming the quantum cloning as a possible eavesdropping attack on quantum communication link, the reversibility can be utilized to improve the security of the link even after the attack.
Cloning machines, that is, transformations that achieve the best approximate copying of a quantum state compatible with the no-cloning theorem, have been a fundamental research topic over the last five years. This study is of particular significance given the close connection between quantum cloning and quantum cryptography: using an optimal cloner generally makes it possible to obtain a tight bound on the best individual eavesdropping strategy in a quantum cryptosystem. In this Chapter, the issue of cloning a continuous-variable quantum system will be analyzed, and a Gaussian cloning transformation will be introduced. This cloner, which copies equally well any two canonically conjugate continuous variables, duplicates all coherent states with a same fidelity (F=2/3). The optical implementation of this cloner and its extension to N-to-M cloners will also be discussed. Finally, the use of this cloner for the security assessment of a quantum key distribution scheme relying on continuous (Gaussian) key carriers will be sketched.
We present here an information theoretic study of Gaussian collective attacks on the continuous variable key distribution protocols based on Gaussian modulation of coherent states. These attacks, overlooked in previous security studies, give a finite advantage to the eavesdropper in the experimentally relevant lossy channel, but are not powerful enough to reduce the range of the reverse reconciliation protocols. Secret key rates are given for the ideal case where Bob performs optimal collective measurements, as well as for the realistic cases where he performs homodyne or heterodyne measurements. We also apply the generic security proof of Christiandl et al. to obtain unconditionally secure rates for these protocols.
We investigate the security against collective attacks of a continuous variable quantum key distribution scheme in the asymptotic key limit for a realistic setting. The quantum channel connecting the two honest parties is assumed to be lossy and imposes Gaussian noise on the observed quadrature distributions. Secret key rates are given for direct and reverse reconciliation schemes including post-selection in the collective attack scenario. The effect of a nonideal error correction and two-way communication in the classical post-processing step is also taken into account.
We address continuous-variable quantum key distribution (QKD) in non-Markovian lossy channels and show how the non-Markovian features may be exploited to enhance security and/or to detect the presence and the position of an eavesdropper along the transmission line. In particular, we suggest a coherent-state QKD protocol which is secure against Gaussian individual attacks based on optimal $1\ensuremath{\rightarrow}2$ asymmetric cloning machines for arbitrarily low values of the overall transmission line. The scheme relies on specific non-Markovian properties, and cannot be implemented in ordinary Markovian channels characterized by uniform losses. Our results give a clear indication of the potential impact of non-Markovian effects in QKD.