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Physics of Particles and Nuclei

The BBGKY Hierarchy of Quantum Kinetic Equations and Its Application in Cryptography

M. Yu. Rasulova

Published Jul 1, 2020• 4 citations
Publisher

Abstract

Abstract In this paper, a new encryption method based on statistical mechanics is proposed, which enables transmitting information without transmitting the encryption key after sending the information, and also makes it possible to determine its own transformation for each information cell. For these purposes, solutions of the Schrödinger equation (Lieb–Liniger model) and a hierarchy of quantum kinetic BBGKY equations with the delta-function potential are used.

DOI
10.1134/s1063779620040619

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Abstract In this paper, a new encryption method based on statistical mechanics is proposed, which enables transmitting information without transmitting the encryption key after sending the information, and also makes it possible to determine its own transformation for each information cell. For these purposes, solutions of the Schrödinger equation (Lieb–Liniger model) and a hierarchy of quantum kinetic BBGKY equations with the delta-function potential are used.
Abstract Cryptography is a scientific method that is used to transmit secret information. In contrast, quantum cryptography depends on physical laws to encrypt information; when the quantum computer appeared, the classic encryption method becomes inefficient. The quantum method is commonly used to distribute keys, a process called as quantum key distribution (QKD). In this paper, we consider the efficiency of the quantum method compared to classical methods. Also, we discuss the security of QKD against several attacks and provide security analysis based on probabilistic models. Additionally, the paper explains how to encrypt random numbers into a sequence of photons using a QKD system for the distribution of a key. This research demonstrates the efficiency and security of QKD in sending and distributing keys between communication parties. Thus, both the sender and the receiver would be able to obtain a security key using the quantum method rather than classical methods.
Transmitting message in secret is getting more and more important nowadays. In the classical world, the message we sent run the risk of being intercepted by an attacker. As a result, we have to encrypt the message, or send it using a private channel. However, if we transmit messages via such methods, there are still some ways to decipher the information. For example, a powerful computer can be used to decrypt the message or try to steal the message from the private channel. In quantum cryptography, entanglement can be used as a secure channel to transmit information with absolute secrecy. From this perspective, quantum entanglement pairs are equivalent to a quantum private key. However, like the classical key distribution problem, the entanglement has to be shared before it can be used. In this paper, we propose a protocol that can be used to distribute such entanglement pairs securely, so they can be subsequently used to transmit messages with perfect security. The security of this protocol is based on the laws of nature, instead of unproven mathematical hard problems.
In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy problems of the BBGKY hierarchy and the dual BBGKY hierarchy in suitable Banach spaces. In the framework of the conventional approach to the description of kinetic evolution the mean-field asymptotics of the quantum BBGKY hierarchy solution is constructed. We develop also alternative approaches. One method is based on the construction of the solution asymptotics of the initial-value problem of the quantum dual BBGKY hierarchy. One more approach is based on the generalized quantum kinetic equation that is a consequence of the equivalence of the Cauchy problems of such evolution equation and the BBGKY hierarchy with initial data determined by the one-particle density operator.
Contemporarily, the quantum world is a new area in physics which has been widely explored. With the contributions of the scholars, the whole structure of the quantum world might cause great revolution on all the knowledge in various fields including teleportation, computing etc. Among various applications, quantum teleportation has attracted plenty of researchers, where remarkable results have been achieved based on the advanced facilities and proposed concepts. For quantum teleportation. The encryption is the key of the process. On this basis, the main topic of the whole paper will demonstrate the possible encryption concluded from two main communication methods. To be specific, the history and basic notes of quantum physics will be recalled primarily. In addition, the principle of encryption and applications of quantum communication will be discussed. Moreover, the state-of-art applications and implementations for encryption of quantum communication will be clarified. These results shed light on guiding further exploration of the encryption process of quantum communication.
Abstract The coordinate Bethe ansatz can be extended to a model, the Lieb–Liniger model, of a one-dimensional gas of Bosons interacting with repulsive δ-function potentials. It has attracted attention due to its relevance for experimental developments in the fields of ultracold gases and optical lattices. This chapter provides an exposition of the related classical nonlinear Schrödinger equation, followed by its generalization to the quantum model. It explores a limiting case, the Tonks-Girardeau gas. The δ-function potentials supply a kind of boundary condition on the wave functions allowing us to analyze the eigenfunctions of the Bethe ansatz, which are examined on the infinite line and for periodic boundary conditions. The latter leads to the Bethe ansatz equations. The solution of these equations is achieved in the thermodynamic limit for the ground state and for low-lying excited states.