Abstract
A bipartite subspace is called strongly positive-partial-transpose (PPT) unextendible if for every positive integer , there is no PPT operator supporting on the orthogonal complement of . 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 system is , 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)].
- Received 7 February 2017
DOI:https://doi.org/10.1103/PhysRevA.95.052346
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