Quantum entropy in terms of local quantum Bernoulli noises and related properties

Abstract

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 ρ_k represented by LQBNs, and define a new quantum entropy $S({\rho }_k)$ based on LQBNs. Furthermore, we demonstrate that this quantum entropy $S({\rho }_k)$ 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 $S({\rho }_k)=k.$

Keywords:

• Localization
• quantum Bernoulli noises
• quantum entropy

2010 MR SUBJECT CLASSIFICATION:

• primary 60H40
• secondary 46E35

Additional information

Funding

The authors are supported by the National Natural Science Foundation of PR China under Grant No. [11861057].