TL;DR
This paper investigates whether local operations and classical communication (LOCC) can approximate the globally optimal measurement for testing the purity of bipartite quantum states when multiple copies are available.
Contribution
It analyzes the asymptotic behavior of LOCC measurements in approximating the optimal global test for quantum state purity.
Findings
LOCC can asymptotically approximate the global optimal measurement
The symmetric subspace projection is optimal with global operations
The study provides bounds on LOCC performance for large n
Abstract
Given n-copies of unknown bipartite (possiblly mixed) state, our task is to test whether the state is a pure state of not. Allowed to use the global operations, optimal one-sided error test is the projection onto the symmetric subspace, obviously. Is it possible to approximate the globally optimal measurement by LOCC when n is large?
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