The quantum entropy cone of stabiliser states

Noah Linden*, František Matúš, Mary Beth Ruskai, Andreas Winter

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

9 Citations (Scopus)

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.

Original languageEnglish
Title of host publication8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages270-284
Number of pages15
Volume22
ISBN (Electronic)9783939897552
DOIs
Publication statusPublished - 1 Nov 2013
Event8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013 - Guelph, Canada
Duration: 21 May 201323 May 2013

Conference

Conference8th Conference on the Theory of Quantum Computation, Communication and Cryptography, TQC 2013
CountryCanada
CityGuelph
Period21/05/1323/05/13

Keywords

  • Entropy inequalities
  • Ingleton inequality
  • Stabiliser states

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