arXiv:1702.07864

Tsallis entropy is natural in the formulation of quantum noise

Boaz Tamir

Published Feb 25, 2017• 1 citation

Abstract

In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information theory. Similarly we redefine entropy exchange and use the same bound.

DOI: 10.48550/arxiv.1702.07864

Related papers

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

Sujuan Zhang, Jing Li

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.

International Journal of Quantum InformationApr 1, 20212 citations

On bounds of Tsallis relative entropy and an inequality for generalized skew information

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.

arXiv:1008.3441Aug 20, 20101 citation

A review of the mathematical properties of the Tsallis entropies

Shigeru Furuichi, Alexander M. Korsunsky

We review the mathematical properties of the generalized entropies, based on our previous papers. This review is an extended version of our article [9]. The Tsallis entropy defined for a quantum state is uniquely derived from three axioms. A generalized Fannes’ inequality is shown. The maximum entropy principle in Tsallis statistics are revisited as an application of the Tsallis relative entropy defined for nonnegative matrices in the framework of matrix analysis. A variational expression for Tsallis relative entropy is derived and some related inequalities are studied. Finally, an application to qunatum information theory is discussed.

AIP conference proceedingsJan 1, 20083 citations

Inequalities for Tsallis relative entropy and generalized skew information

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.

Linear and Multilinear AlgebraSep 23, 201126 citations

Entanglement rates for Rényi, Tsallis, and other entropies

Anna Vershynina

We provide an upper bound on the maximal entropy rate at which the entropy of the expected density operator of a given ensemble of two states changes under nonlocal unitary evolution. A large class of entropy measures in considered, which includes Rényi and Tsallis entropies. The result is derived from a general bound on the trace-norm of a commutator, which can be expected to find other implementations. We apply this result to bound the maximal rate at which quantum dynamics can generate entanglement in a bipartite closed system with Rényi and Tsallis entanglement entropies taken as measures of entanglement in the system.

arXiv:1803.07117Journal of Mathematical PhysicsFeb 1, 201914 citations

Upper continuity bound on the quantum quasi-relative entropy

Anna Vershynina

We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for any operator monotone decreasing function and either mixed qubit or classical states. Moreover, we derive an upper bound for the Umegaki and Tsallis relative entropies in the case of any finite-dimensional states. The bound for the relative entropy improves the known bounds for some states in any dimensions larger than four. The bound for the Tsallis entropy improves the known bounds.

arXiv:1904.00795Journal of Mathematical PhysicsOct 1, 20195 citations