Abstract
It is known that, in an -dimensional quantum system, the maximum dimension of a subspace that contains only entangled states is . We show that the exact same bound is tight if we require the stronger condition that every state with range in the subspace has non-positive partial transpose. As an immediate corollary of our result, we solve an open question that asks for the maximum number of negative eigenvalues of the partial transpose of a quantum state. In particular, we give an explicit method of construction of a bipartite state whose partial transpose has negative eigenvalues, which is necessarily maximal, despite recent numerical evidence that suggested such states may not exist for large and .
- Received 24 May 2013
DOI:https://doi.org/10.1103/PhysRevA.87.064302
©2013 American Physical Society