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.
 Publication:

arXiv eprints
 Pub Date:
 August 2015
 DOI:
 10.48550/arXiv.1508.00860
 arXiv:
 arXiv:1508.00860
 Bibcode:
 2015arXiv150800860O
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 26 pages, 4 figures, 1 table. v2: small corrections throughout + the fourbar linkage