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Infinite Dimensional Analysis Quantum Probability and Related Topics

Entropy exchange and coherent information based on local quantum Bernoulli noises

Qi Han, Shuai Wang, Lijie Gou, Rong Zhang

Published Jul 26, 2024• 4 citations
Publisher

Abstract

Local Quantum Bernoulli Noises (LQBNs) is the localization of Quantum Bernoulli Noises (QBNs), which has high research value in the field of quantum information and has received widespread attention in recent years. In this paper, a new entropy exchange and coherent information with localization characteristics are studied. According to the quantum channel constructed by LQBNs, the relationship between coherent information and coherent mutual entropy with localization characteristics is proved. Finally, we also prove that the coherent information based on LQBNs may disappear.

DOI
10.1142/s0219025724500139

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Local Quantum Bernoulli Noises (LQBNs) is the localization of Quantum Bernoulli Noises (QBNs), which has high research value in the field of quantum information and has received widespread attention in recent years. In this paper, a new entropy exchange and coherent information with localization characteristics are studied. According to the quantum channel constructed by LQBNs, the relationship between coherent information and coherent mutual entropy with localization characteristics is proved. Finally, we also prove that the coherent information based on LQBNs may disappear.
Quantum noise has always been an important issue in the field of quantum information transmission. As the localization of quantum noise, local quantum Bernoulli noises (LQBNs) have attracted extensive attention in recent years. In this paper, the quantum conditional entropy based on LQBNs is deeply discussed, and a new definition of quantum conditional entropy is given. Then we find that this quantum conditional entropy has some basic properties such as concavity, conditional reduced entropy and unitary invariance. This research is of great significance to the field of quantum information, which can help us to understand the influence of local quantum noises on quantum information transmission.
Abstract In the era of rapid development of quantum mechanics, some issues in the field of quantum information have become increasingly important. Local quantum Bernoulli noises (LQBNs) is a localized Bernoulli functional, and it is the localization of quantum Bernoulli noises (QBNs). The distinctive feature of LQBNs lies in its localization properties, which make it highly valuable in the field of quantum information. In this paper, we study three new types of quantum conditional entropy with localization characteristics from three dimensions: local quantum conditional entropy, local quantum conditional entropy at the same position, and classical-quantum conditional entropy. Based on the locality of LQBNs, we prove that the local quantum conditional entropy is concave and unitary invariant. Surprisingly, we find that the local quantum mutual information (entropy) corresponding to the same position is 0. The local quantum conditional entropy defined based on the local quantum state at a specific position, proposed in this paper, provides new insights into understanding the impact of local quantum noise on the information transmission in quantum channels. This discovery not only deepens our understanding of the internal structure of local quantum entropy, but also reveals its influence on the performance of quantum communication.
Localization of quantum Bernoulli noises (LQBNs) are the family of local annihilation and local creation operators acting on Bernoulli functionals. In this paper, we construct a density operator ρk represented by LQBNs, and define a new quantum entropy S(ρk) based on LQBNs. Furthermore, we demonstrate that this quantum entropy S(ρk) also has the basic properties of von Neumann entropy, such as concavity, subadditivity, and nonnegativity. In particular, we obtain the necessary and sufficient condition for S(ρk)=k.
As an important stochastic process, quantum Bernoulli noises has a very important physical background and is an important research object in the field of quantum information. In this paper, we review local quantum Bernoulli noises and local quantum mutual entropy, then introduce quantum channel measurement with local quantum Bernoulli noises. On this basis, we give the channel structure between two systems, and prove the completely positivity of this quantum channel. We also give a channel application on the local quantum mutual entropy.
Abstract In this paper, we first introduce the local quantum information processing task by compressing the density operator based on local quantum Bernoulli noises. Then, the local quantum compression theorem is given, that is, the local quantum entropy is the minimum achievable rate of local compression. Finally, we prove the theorem with the proof of the direct coding theorem and the inverse theorem. The direct coding theorem shows that a scheme with such a local compression rate exists, and that this local compression rate converges to the local quantum entropy. The inverse theorem shows that the compression scheme with the rate below the local entropy is unachievable. With the continuous development of quantum technology, local quantum data compression technology will have broad application prospects and development space.