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Journal of the Optical Society of America B

Methods of decreasing the unambiguous state discrimination probability for subcarrier wave quantum key distribution systems

Andrei Gaidash, Козубов Антон Владимирович, George P. Miroshnichenko

Published Dec 21, 2018• 16 citations
Publisher

Abstract

In this paper, we compare two solutions (well known and newly proposed) for subcarrier wave quantum key distribution systems that decrease the crucial impact of the errorless unambiguous state discrimination attack in order to ensure security in channels with higher losses. One of the well-known methods is based on adding more signal states and allows a decrease in the probability of successful discrimination. However, sifting fractions will decrease too, leading to lower key rates. Thus, we propose a technique that utilizes additional vacuum state (unmodulated carrier and vacuum states at the sidebands) with low a priori sending probability and that provides the same decrease (in the first order) of errorless unambiguous discrimination as for four signal states while maintaining the same sifting fraction as for two states.

DOI
10.1364/josab.36.000b16

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In this paper, we compare two solutions (well known and newly proposed) for subcarrier wave quantum key distribution systems that decrease the crucial impact of the errorless unambiguous state discrimination attack in order to ensure security in channels with higher losses. One of the well-known methods is based on adding more signal states and allows a decrease in the probability of successful discrimination. However, sifting fractions will decrease too, leading to lower key rates. Thus, we propose a technique that utilizes additional vacuum state (unmodulated carrier and vacuum states at the sidebands) with low a priori sending probability and that provides the same decrease (in the first order) of errorless unambiguous discrimination as for four signal states while maintaining the same sifting fraction as for two states.
In this paper, we study unambiguous state discrimination regarding advanced attack on phase-coded quantum key distribution protocol.We propose the method of optimal unambiguous state discrimination probability derivation as a function of a priori probabilities for signal states.The expression obtained as an example in case of two signal states explicitly demonstrates the additional term dependent on small deviations from equal a priori probabilities that may take place in real quantum key distribution implementations.Precise estimation of optimal unambiguous state discrimination probability is significant for complete evaluation of quantum key distribution security.
Abstract Quantum cryptography uses non-orthogonal quantum states, and the eavesdropper cannot extract full information without being detected. Nevertheless, losses in fiber channels allow for additional eavesdropping strategies based on postselective measurements. Here, we study the strategy based on unambiguous discrimination between mixed quantum states, and its partial version with higher success probability. We find information available to the eavesdropper for two protocols of quantum key distribution, namely, geometrically uniform states and subcarrier wave protocols.
We consider an unambiguous state discrimination attack on the B92 protocol of quantum key distribution, realized on the basis of polarization encoding of photons produced by a single-photon source. We calculate the secure key rate and the maximal tolerable loss for various overlaps between two signal states employed in this protocol. We make also a comparison with a physically impossible attack of perfect quantum cloning, and show that the unambiguous state discrimination is much more dangerous for the B92 protocol, than this attack, demonstrating thus, that the security of quantum key distribution is not always based on the no-cloning theorem.
The use of linearly independent signal states in realistic implementations of quantum key distribution (QKD) enables an eavesdropper to perform unambiguous state discrimination. We explore quantitatively the limits for secure QKD imposed by this fact taking into account that the receiver can monitor, to some extent the photon-number statistics of the signals even with todays standard detection schemes. We compare our attack to the beam-splitting attack and show that security against the beam-splitting attack does not necessarily imply security against the attack considered here.
This paper provides an in-depth theoretical analysis of subcarrier multiplexed quantum key distribution (SCM-QKD) systems, taking into account as many factors of impairment as possible and especially considering the influence of nonlinear signal mixing on the end-to-end quantum bit error rate (QBER) and the useful key rate. A detailed analysis of SCM-QKD is performed considering the different factors affecting the sideband visibility (drifts in the modulator bias points, modulation index mismatch between Alice and Bob subcarriers) and the impact of nonlinear signal mixing leaking into otherwise void subcarrier sidebands. In a similar way to classical photonic radio-over-fiber telecommunication and cable TV systems, the impact of this nonlinear signal mixing can be accounted in terms of a quantum carrier to noise ratio that depends on the specific frequency plan that is implemented. QBER and useful key rate results for three different frequency plans featuringNNN$=15(low−countchannelsystem),15 (low-count channel system),15(low−countchannelsystem),N$$=$30 (intermediate-count channel system), and$N$$=50(high−countchannelsystem)channelsareprovided,showingthatphotonnonlinearmixingcanbeofimportanceinmiddle−andhigh−countSCM−QKDsystems(50 (high-count channel system) channels are provided, showing that photon nonlinear mixing can be of importance in middle- and high-count SCM-QKD systems (50(high−countchannelsystem)channelsareprovided,showingthatphotonnonlinearmixingcanbeofimportanceinmiddle−andhigh−countSCM−QKDsystems(N≫30),withmoderateRFmodulationindexes(≫ 30), with moderate RF modulation indexes (≫30),withmoderateRFmodulationindexes(m≫5≫ 5%). In practical terms, nonlinear signal mixing can be neglected if low modulation indexes (≫5m$≪ 2%) are employed to encode the photons in the subcarrier sidebands.