Locality of Orthogonal Product States via Multiplied Copies


الملخص بالإنكليزية

In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyse orthogonal product states in any system to show that with LOCC protocols, to distinguish 7 orthogonal product states, one can exclude 4 states via a single copy. In bipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $left lceil frac {N}{4}right rceil$ copies are allowed, where $left lceil lright rceil$ 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 $left lceil frac {N}{4}right rceil +1$ 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.

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