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Journal of Experimental and Theoretical Physics Letters

On one asymptotic property of time-shift quantum cryptography

S. N. Molotkov

Published Dec 1, 2009• 0 citations
Publisher

Abstract

One of the basic results of classical information theory is that error-free information transmission is possible even through an imperfect binary communication channel with noise up to an error of Q c = 1/2. There is a fundamental and applied question of whether quantum-mechanical constraints can ensure error-free classical-information transmission with quantum states and, moreover, guarantee the security of distributed keys up to the theoretical limit in the error Q c. It has been shown that the secure key distribution is possible up to the error Q c in the asymptotic limit of a large number of bases.

DOI
10.1134/s0021364009190114

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One of the basic results of classical information theory is that error-free information transmission is possible even through an imperfect binary communication channel with noise up to an error of Q c = 1/2. There is a fundamental and applied question of whether quantum-mechanical constraints can ensure error-free classical-information transmission with quantum states and, moreover, guarantee the security of distributed keys up to the theoretical limit in the error Q c. It has been shown that the secure key distribution is possible up to the error Q c in the asymptotic limit of a large number of bases.
The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.
Quantum cryptography involves the fundamental question of the existence of secure protocols of quantum key distribution at any length of a communication channel (at any losses in it). A remarkable feature and novelty of the proposed protocol is that it ensures dual control; first, the intensity of a reference (intense) quantum state is controlled classically before the comparison (measurement) of coherent states from different time windows, and, second, the loss of coherence of a state is detected by interference measurements of an information quantum state and the reference quantum state tested against the conservation of the intensity. Thus, this is the only existing protocol stable to any losses in the communication channel. The length of the communication channel is limited only by dark noise in detectors.
Quantum information theory is a modern branch of theoretical physics. One of its main goals is to interpret concepts of quantum physics. This leads to a deeper understanding of quantum theory. The most common examples of practical applications of basic quantum theory are quantum computation and quantum cryptography. Quantum cryptography provides secure communication between legitimate users even in the presence of an adversary by making possible the distribution of a secret key. It then allows error correction and privacy amplification, which is elimination of adversary information, through classical communication. In this thesis two important aspects of quantum key distribution are covered, namely robustness bounds with respect to provable entanglement for ideal protocols and practical quantum key distribution using two-way classical communication. In part one of the thesis, ideal quantum key distribution protocols and their robustness in terms of provable entanglement are discussed. The robustness bounds are proved for most general coherent attacks. These bounds for provable entanglement are already known to be 25% for the four-state protocol and 33% for the six-state protocol. We anticipate to provide a region in which the legitimate users share entanglement. This region is large for the four-state protocol and is reduced to a smaller region for the six-state protocol because of additional constraint on it. We also investigate the information cost which the adversary has to pay in order to reach these bounds. In part two we adopt a more practical approach. We investigate the limitation on distance of secure communication because of practical restrictions. In particular we investigate the restrictions due to the lack of single photon sources, the lossy channel and faulty detectors. These practical limitations have already been observed using one-way classical communication between legitimate users. It has been observed that it is actually the dark count rate that limit the distance up to which legitimate users can share a secret key. We have used two-way classical communication to postpone the effect of dark counts and increase the distance to considerable amount. For the purpose we have considered an optimal attack with respect to the disturbance that an eavesdropper creates while attacking. Any other format of attacking will increase the disturbance. We show that using two-way classical communication for post processing we can increase the distance of secure communication considerably.
Quantum key distribution (QKD) enables information-theoretic secure communication, yet its ultimate tolerance to noise and achievable transmission distance remain fundamentally constrained. We establish the maximum quantum bit error rate (QBER) compatible with secure QKD and derive corresponding upper bounds on communication distance. Our results follow from a fundamental capacity threshold for qubit Pauli channels and apply to protocols based on two or more mutually unbiased bases, using either single-photon or weak coherent sources. By connecting information-theoretic limits to realistic physical noise models, we obtain universal bounds on achievable distances in fiber and free-space links, including diffraction-limited constraints relevant to deep-space quantum communications. These findings clarify the ultimate noise robustness of QKD and delineate the fundamental boundaries of secure quantum communication.
The stability of quantum key distribution systems is based not only on the detection of attacks on quantum states, which is guaranteed by the fundamental quantum theory laws, but also on ensuring the integrity of classical messages transmitted through an auxiliary classical communication channel. To detect attacks on the classic communication channel, the authentication procedure is used. Information-theoretic authentication guarantees the detection of attacks on the classical communication channel regardless of the computational and technical capabilities of an eavesdropper, including the quantum computer. The fundamental quantum cryptographic relationship between the abstract criterion of the robustness of quantum key distribution systems with theoretical-information authentication and the quantum key search complexity has been determined for the first time using simple means.
In the present times, the demand for sophisticated encryption methods has escalated, especially for securing data transmission in vulnerable environments. These methods leverage diverse algorithms to fortify the integrity of communication channels. Quantum mechanics plays a pivotal role in two specific areas: quantum key distribution and property-based cryptography, both of which contribute to establishing secure communication protocols. This study focuses on conducting a comparative evaluation of classical and quantum cryptography, employing various cryptography algorithms. The objective is to ascertain the optimal algorithm within each realm classical and quantum cryptography for ensuring robust security.