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A new axiomatic characterization of the von Neumann entropy

Wilhelm Ochs

Reports on Mathematical PhysicsAug 1, 197543 citations

Infinitely Many Constrained Inequalities for the von Neumann Entropy

Josh Cadney, Noah Linden, Andreas Winter

We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new inequalities were proved originally by Makarychevfor the Shannon entropy, using properties of probability distributions. Our approach extends the proof of the inequalities to the quantum domain, and includes their independence for the quantum and also the classical cases.We exhibit infinitely many new, constrained inequalities for the von Neumann entropy, and show that they are independent of each other and the known inequalities obeyed by the von Neumann entropy (basically strong subadditivity). The new inequalities were proved originally by Makarychevfor the Shannon entropy, using properties of probability distributions. Our approach extends the proof of the inequalities to the quantum domain, and includes their independence for the quantum and also the classical cases.

arXiv:1107.0624IEEE Transactions on Information TheoryJan 18, 201241 citations

On the characterization of the von Neumann entropy via the entropies of measurements

P. Staszewski

Reports on Mathematical PhysicsFeb 1, 19783 citations

Von Neumann Entropy by Logarithmic Method

Bijan Nikouravan

The Von Neumann entropy plays a central role in the quantum information theory and is a concave function and following the property . In this paper, we introduce a new proof for the linearity of Von Neumann entropy in the rate without using the above inequality. Here the Von Neumann entropy is concave; that is, given weights and density matrices . Roughly speaking, we will show that in the rate case, the Von Neumann entropy is linear without using Fannes inequality. https://orcid.org/0000-0003-4308-1632The Von Neumann entropy plays a central role in the quantum information theory and is a concave function and following the property . In this paper, we introduce a new proof for the linearity of Von Neumann entropy in the rate without using the above inequality. Here the Von Neumann entropy is concave; that is, given weights and density matrices . Roughly speaking, we will show that in the rate case, the Von Neumann entropy is linear without using Fannes inequality. https://orcid.org/0000-0003-4308-1632

International Journal of Fundamental Physical SciencesDec 1, 20191 citation

Continuity of the von Neumann Entropy

Максим Евгеньевич Широков

arXiv:0904.1963Communications in Mathematical PhysicsFeb 28, 201032 citations

Remainder terms for some quantum entropy inequalities

Eric A. Carlen, Élliott H. Lieb

We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.

arXiv:1402.3840Journal of Mathematical PhysicsApr 1, 201443 citations

A New Inequality for the von Neumann Entropy

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