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Scientific Reports

Quantum channel measurement with local quantum Bernoulli noises

Qi Han, Yanan Han, Yaxin Kou, Ning Bai

Published Jul 28, 2022• 9 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-022-17268-y

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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.
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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.
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.
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 a peculiar resource of quantum mechanics, quantum correlation has been applied to many aspects. In quantum information processing and quantum computing, the quantum correlation plays an extremely important role, and it has been a subject of further studies, principally due to the general belief that it is a fundamental resource for different quantum information processing tasks. In addition, correlation measure is a very important physical quantity in studying the quantum correlation. A well-defined correlation measure needs to have some necessary properties. By proving these necessary properties, we can deepen our understanding of correlation measure. As one of the key concepts of quantum information theory, relative entropy is always used to measure the uncertainty contained in the state of physical system. In order to better understand the properties and applications of correlation measure based on relative entropy, in this paper, according to the properties of the min relative entropy, we give the quantum correlation measure based on min relative entropy for two-partition and k-partition. Furthermore, we prove that it satisfies some necessary properties of quantum correlation measures, including the nonnegativity, the invariance under local unitary operators, and the monotonicity under completely positive trace-preserving. By proving these properties, we show that the given correlation measure is well-defined. Security of communication has received much attention since ancient times. In today's society, the internet, instant messaging and e-commerce applications are all related to the information security, and the information security is related to the vital interests of everyone. The information encryption is one of the important methods to ensure information security. As an important way to ensure information security, quantum channel has received more and more attention. At the end of the paper, we introduce the concept of quantum channel, and discuss the influence of quantum channel on the correlation measure based on min relative entropy under k-partition. By proposing a new correlation measure and proving the effect quantum channel on the measure, we can better describe the uncertainty contained in the state of physical system.