Locality of orthogonal product states via multiplied copies
College of Mathematics, South China University of Technology, 510641, Guangzhou, People’s Republic of China
Accepted: 12 October 2021
Published online: 22 November 2021
In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyze orthogonal product states in any system to show that with LOCC protocols, to distinguish seven orthogonal product states, one can exclude four states via a single copy. In bipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if copies are allowed, where for a real number l means the smallest integer not less than l. In multipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if copies are allowed. We also give a theorem to show how many states can be excluded via a single copy if we are distinguishing n orthogonal product states by LOCC protocols in a bipartite system. Not like previous results, our result is a general result for any set of orthogonal product states in any system.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021