On Positive Partial Transpose Matrices

Partial Transpose of Permutation Matrices

The main purpose of this paper is to look at the notion of partial transpose from the combinatorial side. In this perspective, we solve some basic enumeration problems involving partial transpose of permutation matrices. Specifically, we count the number of permutations matrices which are invariant under partial transpose. We count the number of permutation matrices which are still permutation ...

Witness for an entangled state with positive partial transpose

In this letter we have analyzed an entangled state in C3 ⊗ C3 having a positive partial transposition and have shown that it is an edge state. Further we have constructed explicitly a witness operator W which detects the entanglement. PACS numbers: 03.67.-a

Entanglement cost under positive-partial-transpose-preserving operations.

We study the entanglement cost under quantum operations preserving the positivity of the partial transpose (PPT operations). We demonstrate that this cost is directly related to the logarithmic negativity, thereby providing the operational interpretation for this entanglement measure. As examples we discuss general Werner states and arbitrary bipartite Gaussian states. Then we prove that for th...

Transpose Matrices and Groups of Permutations

For simplicity we follow a convention: x, x1, x2, y1, y2 are arbitrary, i, j, k, n, m are natural numbers, D is a non-empty set, K is a field, s is a finite sequence, and a, b, c, d are elements of D. The scheme SeqDEx concerns a non-empty set A, a natural number B, and a binary predicate P, and states that: there exists a finite sequence p of elements of A such that dom p = SegB and for every ...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces