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arXiv · 1302.5453

The Quantum Entropy Cone of Stabiliser States

Noah Linden·František Matúš·Mary Beth Ruskai·Andreas Winter
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Abstract

We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the classic inequalities, a type of linear rank inequalities associated with the combinatorial structure of normal subgroups of certain matrix groups. In the 4-party case, there is only one such inequality, the so-called Ingleton inequality. For these systems we show that strong subadditivity, weak monotonicity and Ingleton inequality exactly characterize the entropy cone for stabiliser states.

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Noah Linden, František Matúš, Mary Beth Ruskai, Andreas Winter. 2013-07-02. The Quantum Entropy Cone of Stabiliser States. https://doi.org/10.4230/lipics.tqc.2013.270

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