Infinitely many constrained inequalities for the von Neumann entropy

Details Infinitely many constrained inequalities for the von Neumann entropy Infinitely many constrained inequalities for the von Neumann entropy

2011-07-04

arxiv.org/abs/1107.0624v1

Physics

Quantum Physics

11 pages

Scientific paper

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 Makarychev et al. [Commun. Inf. Syst., 2(2):147-166, 2002] for 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.

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