The Quantum Entropy Cone of Stabiliser States
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.
Keywords
Cite
@article{arxiv.1302.5453,
title = {The Quantum Entropy Cone of Stabiliser States},
author = {Noah Linden and František Matúš and Mary Beth Ruskai and Andreas Winter},
journal= {arXiv preprint arXiv:1302.5453},
year = {2013}
}
Comments
15 pages, uses lipics.cls (http://www.dagstuhl.de/en/publications/lipics). V2 is the final TQC 2013 proceedings version, it has numerous corrections, updated references, and a new co-author