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DOI: 10.4230/LIPIcs.TQC.2013.270
URN: urn:nbn:de:0030-drops-43278
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4327/
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Linden, Noah ; Matus, Frantisek ; Ruskai, Mary Beth ; Winter, Andreas

The Quantum Entropy Cone of Stabiliser States

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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.

BibTeX - Entry

@InProceedings{linden_et_al:LIPIcs:2013:4327,
  author =	{Noah Linden and Frantisek Matus and Mary Beth Ruskai and Andreas Winter},
  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 =	{Simone Severini and Fernando Brandao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4327},
  URN =		{urn:nbn:de:0030-drops-43278},
  doi =		{10.4230/LIPIcs.TQC.2013.270},
  annote =	{Keywords: Entropy inequalities, Stabiliser states, Ingleton inequality}
}

Keywords: Entropy inequalities, Stabiliser states, Ingleton inequality
Seminar: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Issue Date: 2013
Date of publication: 05.11.2013


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