How to combine three quantum states
Abstract
We devise a ternary operation for combining three quantum states: it consists of permuting the input systems in a continuous fashion and then discarding all but one of them. This generalizes a binary operation recently studied by Audenaert et al. [arXiv:1503.04213] in the context of entropy power inequalities. Our ternary operation continuously interpolates between all such nested binary operations. Our construction is based on a unitary version of Cayley's theorem: using representation theory we show that any finite group can be naturally embedded into a continuous subgroup of the unitary group. Formally, this amounts to characterizing when a linear combination of certain permutations is unitary.
Cite
@article{arxiv.1508.00860,
title = {How to combine three quantum states},
author = {Maris Ozols},
journal= {arXiv preprint arXiv:1508.00860},
year = {2017}
}
Comments
26 pages, 4 figures, 1 table. v2: small corrections throughout + the four-bar linkage