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

Understand

A bipartite subspace $S$ is called strongly positive-partial-transpose-unextendible (PPT-unextendible) if for every positive integer $k$, there is no PPT operator supporting on the orthogonal complement of $S^{\otimes k}$.

• 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.