Quantum conditional entropy and classical-quantum conditional entropy with localization characteristics

Abstract

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.