Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.
Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.
Purpose of work is to review new aspects for the task of information extraction from ensembles of quantum states, dictated by practical tasks of quantum cryptography. Research methods: mathematical methods of quantum information theory, in particular, unambiguous discrimination of quantum states. Results of the study: the paper analyzes the literature on the topic of eavesdropper information bounds in quantum cryptography in the presence of channel attenuation, including in the absence of quantum memory. The features of application of the fundamental information bound to the eavesdropper information in the presence of attenuation, the threats of application of ad hoc countermeasures for unambiguous state discrimination attack are demonstrated. The problems of finding an effective postselective eavesdropping transformation, as well as measurement in the absence of eavesdropper’s quantum memory, are formulated. Scientific novelty: the scientific novelty consists in the integration of disparate approaches to the problem of eavesdropper information bounds in quantum cryptography and resisting attacks in case of lossy channel. The review describes the peculiarities of applying information bound to quantum cryptography problems and formalizes the challenges facing the eavesdropper under attenuation conditions.
Abstract Symmetric coherent states are of interest in quantum cryptography, since for such states there is an upper bound for unambiguous state discrimination (USD) probability, which is used to resist USD attack. But it is not completely clear what an eavesdropper can do for shorter channel length, when USD attack in not available. We consider the task of generalized discrimination between symmetric coherent states and construct an operation which enlarges the information content of the states with fixed failure probability. We apply this transformation to develop a zero-error eavesdropping strategy for quantum cryptography on symmetric coherent states.
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.
An attempt to eavesdrop on a quantum cryptographic channel reveals itself through errors it inevitably introduces into the transmission. We investigate the relationship between the induced error rate and the maximum amount of information the eavesdropper can extract, in both the two-state B92 [B92 refers to the work of C. H. Bennett, Phys. Rev. Lett. 68, 3121 (1992)] and the four-state BB84 [BB84 refers to the work of C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175--179] quantum cryptographic protocols. In each case, the optimal eavesdropping method that on average yields the most information for a given error rate is explicitly constructed. Analysis is limited to eavesdropping strategies where each bit of the quantum transmission is attacked individually and independently from other bits. Subject to this restriction, however, we believe that all attacks not forbidden by physical laws are covered. Unlike previous work, the eavesdropper's advantage is measured in terms of Renyi (rather than Shannon) information, and with respect only to bits received error-free by Bob (rather than all bits). This alters both the maximum extractable information and the optimal eavesdropping attack. The result can be used directly at the privacy amplification stage of the protocol to accomplish secure communication over a noisy channel.
Abstract Early security proofs of the keys in quantum cryptography systems were based on the assumption that the transmitting and receiving stations were completely isolated from the outside world—the eavesdropper. However, this condition cannot be implemented in practice, since quantum cryptography systems are open systems, in the sense that an eavesdropper can have indirect access, for example, through a fiber communication channel to critical equipment elements (phase modulators, intensity modulators, etc) using active sensing of the state of these elements—Trojan-horse attacks. A new Trojan-horse attack based on joint unambiguous measurements of reflected probing states from an intensity modulator and information states in a quantum communication channel is proposed. Estimates of attack parameters for a number of quantum key distribution protocols are given, when an attack leads to compromise of keys.
Quantum cryptography converts structural restrictions on quantum information into operational secrecy. This article develops the chain connecting nonorthogonal-state discrimination, trace distance and fidelity, the Helstrom bound, no-cloning, no-broadcasting, information-disturbance relations, conditional entropy, and privacy amplification. A linearity argument proves that no universal device can copy arbitrary pure states, while the mixed-state no-broadcasting theorem identifies pairwise commutativity as the exact boundary of exact broadcastability. These results explain why an eavesdropper cannot retain a perfect replica of every signal and wait for later basis disclosure. They are not, however, complete security proofs. Modern quantum key distribution must cover coherent attacks, quantum memory, public reconciliation leakage, imperfect sources and detectors, finite samples, authentication, and composition with later applications. The review connects state discrimination to adversarial guessing probability through conditional min-entropy and explains how entropic uncertainty and entanglement-based reductions transform observed statistics into a lower bound on extractable key. Approximate cloning, unambiguous discrimination, channel loss, side channels, and device-independent certification are examined as qualifications to elementary intuition. The central result is a hierarchy: nonorthogonality restricts distinguishability; data processing forbids perfect information amplification; parameter estimation bounds an adversary’s conditional states; and quantum-proof hashing yields a key close in trace distance to an ideal independent key. Cryptographic security therefore depends on quantum limitations embedded within a fully specified protocol and adversarial model.