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DOI: 10.4230/LIPIcs.TQC.2013.270
URN: urn:nbn:de:0030-drops-43278
URL: https://drops.dagstuhl.de/opus/volltexte/2013/4327/
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: | 13.11.2013 |
