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DOI: 10.4230/LIPIcs.TQC.2013.270
The Quantum Entropy Cone of Stabiliser States

Authors: Noah Linden, Frantisek Matus, Mary Beth Ruskai, and Andreas Winter

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

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.
Cite as

Noah Linden, Frantisek Matus, Mary Beth Ruskai, and Andreas Winter. The Quantum Entropy Cone of Stabiliser States. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 270-284, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{linden_et_al:LIPIcs.TQC.2013.270,
  author =	{Linden, Noah and Matus, Frantisek and Ruskai, Mary Beth and Winter, Andreas},
  title =	{{The Quantum Entropy Cone of Stabiliser States}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{270--284},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.270},
  URN =		{urn:nbn:de:0030-drops-43278},
  doi =		{10.4230/LIPIcs.TQC.2013.270},
  annote =	{Keywords: Entropy inequalities, Stabiliser states, Ingleton inequality}
}
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