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Nanosystems Physics Chemistry Mathematics

Analysis of the unambiguous state discrimination with unequal a priori probabilities

Andrei Gaidash, S.S. Medvedeva, George P. Miroshnichenko

Published Aug 30, 2019• 3 citations
Publisher

Abstract

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.

DOI
10.17586/2220-8054-2019-10-4-398-401

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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.
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.
Abstract In this paper we investigate the advanced unambiguous state discrimination (USD) attack that is crucial for quantum key distribution based on phase-coded coherent states. Performing the attack Eve imposes all discriminated states while she can maintain both detection and error rates at Bob’s side. In this work we give the detailed description of the attack and propose the general approach for countermeasures. As the particular case we introduce the so-called ‘mousetrap’ (uninformative) state which allows to decrease the USD probability and preserve high sifted key rate. We also propose some candidates for ‘mousetrap’ states and provide the estimation on the discrimination probability for each of them.
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.
Considering quantum detection, there are two different ways to make a measurement on signals set. One is minimum error discrimination and another is unambiguous states discrimination. In this work, we study the unambiguous state discrimination of coherent states. The quantum measurement model investigated is based on binary signals. All necessary positive-operator valued measurements are established to implement the quantum measurements in non-ambiguity way. The conclusive probability and inconclusive probability for the unambiguous discrimination of both on-off keying and binary-phase-shifting keying modulations are derived rigorously to show the measurement performance of proposed detection method theoretically.
Considering quantum detection, there are two different ways to make a measurement on signals set. One is minimum error discrimination and another is unambiguous states discrimination. In this work, we study the unambiguous state discrimination of coherent states. The quantum measurement model investigated is based on binary signals. All necessary positive-operator valued measurements are established to implement the quantum measurements in non-ambiguity way. The conclusive probability and inconclusive probability for the unambiguous discrimination of both on-off keying and binary-phase-shifting keying modulations are derived rigorously to show the measurement performance of proposed detection method theoretically.