An operator inequality

TL;DR: This document focuses on translating various information-theoretic measures of distinguishability for probability distributions into measures of distin- guishability for quantum states, and gives a way of expressing the problem so that it appears as algebraic as that of the problem of finding quantum distinguishability measures.

TL;DR: Jensen's operator inequality and Jensen's trace inequality for real functions defined on an interval are established in what might be called their definitive versions in this paper, which is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions considered in earlier versions of the theory by the authors.

TL;DR: In this article, the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval were established by introducing genuine non-commutative convex combinations of operators, as opposed to the contractions used in earlier versions of the theory.

TL;DR: In this paper, it was shown that for any pair A, B of n × n complex matrices there is a unitary matrix U, depending on A and B, such that p, q > 0 satisfy 1/p + 1/q = 1.

TL;DR: In this article, a short proof is given based on C*-algebra theory for the well-known theorem that if S and Tare bounded selfadjoint operators on a Hubert space such that 0^5^T then Sai|7"a for each 0^a 0; and S+e/and T+el are both invertible.