Remainder Terms for Some Quantum Entropy Inequalities

Abstract

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.

6 pages, latex

References in corpus (4)

• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• Inequalities for Quantum Entropy: A Review with Conditions for Equality
• A Unified Treatment of Convexity of Relative Entropy and Related Trace Functions, with Conditions for Equality
• Bounds for Entanglement via an Extension of Strong Subadditivity of Entropy

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• More on a trace inequality in quantum information theory
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