A trace inequality arising from quantum information theory

Christopher King

Shigeru Furuichi

Quantum entropy and skew information play important roles in quantum information science. They are defined by the trace of the positive operators so that the trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this paper, we study some properties for information quantities in quantum system through trace inequalities. Especially, we give upper bounds and lower bounds of Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum system. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.

Debashree Chakraborty

Shigeru Furuichi

Quantum entropy and skew information play important roles in quantum information science. They are defined by traces of positive operators, hence trace inequalities often have important roles to develop the mathematical theory in quantum information science. In this article, we study some properties for information quantities in quantum systems through trace inequalities. Especially, we give upper bounds and lower bounds on the Tsallis relative entropy, which is a one-parameter extension of the relative entropy in quantum systems. In addition, we compare the known bounds and the new bounds, for both upper and lower bounds, respectively. We also give an inequality for generalized skew information by introducing a generalized correlation measure.

Bo Liu

For selfadjoint matrices ρ and X,a skew information of Lieb's type Sf,g(ρ,X) is positive or negative if some conditions for realvalued(continuous) f and g is given.As another important application,yanagi trace inequality can be settled.That is,for positive matrices A and B,if every real number s,then Tr{(A+B)s[A(logA)2+B(logB)2]-(A+B)s-1(AlogA+BlogB)2}≥0 where 0≤s≤1.

Runyao Duan, Zhengfeng Ji, Yuan Feng +1 more