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arXiv:quant-ph/9910106 · Physical Review A

Unambiguous state discrimination in quantum cryptography with weak coherent states

Miloslav Dušek, Mika O. Jahma, Norbert Lütkenhaus

Published Jul 13, 2000• 160 citations
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Abstract

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.

DOI
10.1103/physreva.62.022306

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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.
In this paper, we investigate limitations imposed by sequential attacks on the performance of a differential-phase-shift (DPS) quantum key distribution (QKD) protocol with weak coherent pulses. Specifically, we analyze a sequential attack based on optimal unambiguous discrimination of the relative phases between consecutive signal states emitted by the source. We show that this attack can provide tighter upper bounds for the security of a DPS QKD scheme than those derived from sequential attacks where the eavesdropper aims to identify the state of each signal emitted by the source unambiguously.
We analyze realistic vulnerabilities of decoy-state quantum key distribution (QKD) arising from the combination of laser damage attack (LDA) and unambiguous state discrimination (USD). While decoy-state QKD is designed to protect against photon-number-splitting and beam-splitting attacks by accurately estimating the single-photon fraction, it relies on stable attenuation to prepare pulses with fixed mean-photon numbers. An eavesdropper (Eve) can exploit LDA to irreversibly alter the optical components on Alice's side, effectively increasing the mean-photon numbers beyond the decoy-state security regime. We show that once the alteration exceeds a critical threshold-on the order of 10-20 dB-Eve can implement an efficient USD-based intercept-resend strategy using current off-the-shelf technology, thus obtaining the entire secret key. Numerical simulations confirm that for sufficiently elevated mean-photon numbers, Eve's conclusive measurement outcomes skew the decoy-state statistics, yet remain undetected by standard security checks. We further demonstrate how a modified USD setup employing an additional beam splitter can reduce the required threshold, facilitating Eve's attack. Additionally, we introduce the pseudo-photon-number resolution USD attack, which allows Eve to emulate all observable gains at Bob's side so that she remains fully undetectable even with advanced statistical checks. Our findings emphasize the need for robust safeguards against high-power laser damage in QKD systems, including careful hardware selection, rigorous testing under high-power illumination, and real-time monitoring to ensure the integrity of the decoy-state protocol.
It is impossible to distinguish a set of linearly dependent quantum states, which ensures the security of quantum key distribution (QKD). When considering some features such as symmetry, one may distinguish a part of the quantum states from another part, called ambiguous discrimination. In this paper, we demonstrate that two-way deterministic QKD (TDQKD) is immune to photon-number-splitting (PNS) attacks for two-photon signals. When there are three or more photons in signals, the eavesdropper can gain the key bits probabilistically, without introducing any error rate. When the average number of photons per pulse takes the value of 0.1, the successful probability of PNS attacks on nonempty pulses is about 0.001, and the corresponding channel loss is about 30 dB. Our results show that TDQKD is robust against PNS attacks.
Abstract Quantum key distribution (QKD) is a quantum technology which creates a common secret key between two distant users without any technological and computational assumptions about the eavesdropper. Nevertheless, not all the QKD protocols have tight upper and lower security bounds, thus the study of eavesdropping strategies and countermeasures is important. Using large number of symmetric coherent states is one of possible technologies in quantum key distribution against unambiguous state discrimination (USD) attack. Here we propose an attack based on heterodyne measurement, which is relatively simple for practical implementation and which becomes more powerful than USD attack when the number of states in the protocol is large enough. We study the performance of this attack for various symmetric coherent states QKD protocol parameters and for various distances between the legitimate users.
We discuss several methods for unambiguous state discrimination of N symmetric coherent states using linear optics and photodetectors. One type of measurement is shown to be optimal in the limit of small photon numbers for any N. For the special case of N=4N=4N=4 this measurement can be fruitfully used by the receiving end (Bob) in an implementation of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol using faint laser pulses. In particular, if Bob detects only a single photon the procedure is equivalent to the standard measurement that he would have to perform in a single-photon implementation of BB84, if he detects two photons Bob will unambiguously know the bit sent to him in 50% of the cases without having to exchange basis information, and if three photons are detected, Bob will know unambiguously which quantum state was sent.
It is shown that the quantum cryptography protocol on geometrically uniform coherent states, which uses the restriction for unambiguous discrimination of a set of symmetric coherent states and allows resisting an unambiguous state discrimination attack (USD attack), is not secure to a number of other attacks. The key length formula from the work of S.N. Molotkov [ JETP Lett. , 101 (8), 579 (2015) ] and the key generation rate for a number of constructive attacks of the eavesdropper are compared and it is shown that the key generation rate in this work is significantly overestimated. This leads to the fact that the distributed key is not secret.