[en] Any key-generation session contains a finite number of quantum-state messages, and it is there-fore important to understand the fundamental restrictions imposed on the minimal length of a string required to obtain a secret key with a specified length. The entropy uncertainty relations for smooth min and max entropies considerably simplify and shorten the proof of security. A proof of security of quantum key distribution with phase-temporal encryption is presented. This protocol provides the maximum critical error compared to other protocols up to which secure key distribution is guaranteed. In addition, unlike other basic protocols (of the BB84 type), which are vulnerable with respect to an attack by “blinding” of avalanche photodetectors, this protocol is stable with respect to such an attack and guarantees key security.

[en] The fundamental quantum mechanics prohibitions on the measurability of quantum states allow secure key distribution between spatially remote users to be performed. Experimental and commercial implementations of quantum cryptography systems, however, use components that exist at the current technology level, in particular, one-photon avalanche photodetectors. These detectors are subject to the blinding effect. It was shown that all the known basic quantum key distribution protocols and systems based on them are vulnerable to attacks with blinding of photodetectors. In such attacks, an eavesdropper knows all the key transferred, does not produce errors at the reception side, and remains undetected. Three protocols of quantum key distribution stable toward such attacks are suggested. The security of keys and detection of eavesdropping attempts are guaranteed by the internal structure of protocols themselves rather than additional technical improvements.

[en] The proof of the security of quantum key distribution is a rather complex problem. Security is defined in terms different from the requirements imposed on keys in classical cryptography. In quantum cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper after key distribution to an ideal quantum state that is uncorrelated to the key of legitimate users. A metric of closeness between two quantum states is given by the trace metric. In classical cryptography, the security of keys is understood in terms of, say, the complexity of key search in the presence of side information. In quantum cryptography, side information for the eavesdropper is given by the whole volume of information on keys obtained from both quantum and classical channels. The fact that the mathematical apparatuses used in the proof of key security in classical and quantum cryptography are essentially different leads to misunderstanding and emotional discussions [1]. Therefore, one should be able to answer the question of how different cryptographic robustness criteria are related to each other. In the present study, it is shown that there is a direct relationship between the security criterion in quantum cryptography, which is based on the trace distance determining the distinguishability of quantum states, and the criterion in classical cryptography, which uses guesswork on the determination of a key in the presence of side information.

[en] A lower bound is obtained for the photon arrival-time-energy uncertainty relation

[en] Relationship is established between the security of the BB84 quantum key distribution protocol and the forward and converse coding theorems for quantum communication channels. The upper bound Q_c ∼ 11% on the bit error rate compatible with secure key distribution is determined by solving the transcendental equation H(Q_c)=C-bar(ρ)/2, where ρ is the density matrix of the input ensemble, C-bar(ρ) is the classical capacity of a noiseless quantum channel, and H(Q) is the capacity of a classical binary symmetric channel with error rate Q

[en] A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. It is shown that the maximum tolerable error rate for this protocol depends on the counting rate in the control time slot. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability

[en] Quantum mechanics admits collective measurements that are related to the projection onto entangled states and allow one to retrieve more classical information from an ensemble of quantum states compared with individual measurements. In this relation, a fundamental question arises for key secrecy in quantum cryptography. Should the secrecy criterion be formulated with regard to all keys distributed both on previous and future quantum key distribution (QKD) sessions, or it suffices to guarantee key secrecy only in an individual QKD session? The study of this question is the subject of the present paper.

[en] A cryptographic analysis is presented of a new quantum key distribution protocol using phase-time coding. An upper bound is obtained for the error rate that guarantees secure key distribution. It is shown that the maximum tolerable error rate for this protocol depends on the counting rate in the control time slot. When no counts are detected in the control time slot, the protocol guarantees secure key distribution if the bit error rate in the sifted key does not exceed 50%. This protocol partially discriminates between errors due to system defects (e.g., imbalance of a fiber-optic interferometer) and eavesdropping. In the absence of eavesdropping, the counts detected in the control time slot are not caused by interferometer imbalance, which reduces the requirements for interferometer stability.

[en] Since a strictly single-photon source is not yet available, in quantum cryptography systems, one uses, as information quantum states, coherent radiation of a laser with an average number of photons of μ ≈ 0.1–0.5 in a pulse, attenuated to the quasi-single-photon level. The linear independence of a set of coherent quasi-single-photon information states leads to the possibility of unambiguous measurements that, in the presence of losses in the line, restrict the transmission range of secret keys. Starting from a certain value of critical loss (the length of the line), the eavesdropper knows the entire key, does not make errors, and is not detected—the distribution of secret keys becomes impossible. This problem is solved by introducing an additional reference state with an average number of photons of μ_c_l ≈ 10"3–10"6, depending on the length of the communication line. It is shown that the use of a reference state does not allow the eavesdropper to carry out measurements with conclusive outcome while remaining undetected. A reference state guarantees detecting an eavesdropper in a channel with high losses. In this case, information states may contain a mesoscopic average number of photons in the range of μ_q ≈ 0.5–10"2. The protocol proposed is easy to implement technically, admits flexible adjustment of parameters to the length of the communication line, and is simple and transparent for proving the secrecy of keys.

[en] A quantum key distribution (QKD) protocol with nonbinary encoding is proposed that admits an exact proof of secrecy. The protocol provides higher rate of key generation compared with the BB84 protocol and, moreover, has a simple experimental implementation without active elements on the receiver side, that does not require polarization matching at the output of the communication line.