Indistinguishability of bipartite states by positive-partial-transpose operations in the many-copy scenario

© 2017 American Physical Society. A bipartite subspace S is called strongly positive-partial-transpose (PPT) unextendible if for every positive integer k, there is no PPT operator supporting on the orthogonal complement of S - k. We show that a subspace is strongly PPT unextendible if it contains a PPT-definite operator (a positive semidefinite operator whose partial transpose is positive definite). Based on these, we are able to propose a simple criterion for verifying whether a set of bipartite orthogonal quantum states is indistinguishable by PPT operations in the many-copy scenario. Utilizing this criterion, we further point out that any entangled pure state and its orthogonal complement cannot be distinguished by PPT operations in the many-copy scenario. On the other hand, we investigate that the minimum dimension of strongly PPT-unextendible subspaces in an m - n system is m+n-1, which involves a generalization of the result that non-positive-partial-transpose subspaces can be as large as any entangled subspace [N. Johnston, Phys. Rev. A 87, 064302 (2013)PLRAAN1050-294710.1103/PhysRevA.87.064302]