0399530 20240103203337.820131203235959.9 84908223113 10.4230/LIPIcs.TQC.2013.270 15 s. E cav_un_epca*0399712978-3-939897-55-21868-8969270-284DagstuhlSchloss Dagstuhl-Leibniz-Zentrum fuer Informatik2013SeveriniS.BrandaoF. Entropy inequalities Stabiliser states Ingleton inequality cav_un_auth*0297028 Linden N. GB cav_un_auth*0101161 Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Matúš František UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0297029 Ruskai M. B. CA cav_un_auth*0297030 Winter A. GB http://library.utia.cas.cz/separaty/2013/MTR/matus-0399530.pdf cav_un_auth*0292670 GA13-20012S GA ČR 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. cav_un_auth*0296881 Conference on Theory of Quantum Computation, Communication and Cryptography /8./ 2013 Guelph CA BA 2014 4 PR RVO:67985556 http://hdl.handle.net/11104/0226948 2013 84908223113 SCOPUS cav_un_epca*0399712 Proceedings of the 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) 978-3-939897-55-2 1868-8969 270 284 Dagstuhl Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik 2013 Leibniz International Proceedings in Informatics 22 Severini S. 340 Brandao F. 340