A bound on expectation values and variances of quantum observables via Rényi entropy and Tsallis entropy

Author:

Zhang Sujuan12,Li Jing2

Affiliation:

1. Postdoctoral Research Station of Mathematics, Hebei Normal University, Shijiazhuang, Hebei 050024, People’s Republic of China

2. Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, People’s Republic of China

Abstract

Entropy is a key concept of quantum information theory. The entropy of a quantum system is a measure of its randomness and has many applications in quantum communication protocols, quantum coherence, and so on. In this paper, based on the Rényi entropy and Tsallis entropy, we derive the bounds of the expectation value and variance of a quantum observable. By the maximal value of Rényi entropy, we show an upper bound on the product of variance and entropy. Furthermore, we obtain the reverse uncertainty relation for the product and sum of the variances for [Formula: see text] observables respectively.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Physics and Astronomy (miscellaneous)

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