Y. -J. Han, X. J. Ren, Y. C. Wu, G. -C. Guo
Published 2006-09-12Version 1
Many of the properties of the partial transposition are not clear so far. Here the number of the negative eigenvalues of K(T)(the partial transposition of K) is considered carefully when K is a two-partite state. There are strong evidences to show that the number of negative eigenvalues of K(T) is N(N-1)/2 at most when K is a state in Hilbert space N*N. For the special case, 2*2 system(two qubits), we use this result to give a partial proof of the conjecture sqrt(K(T))(T)>=0. We find that this conjecture is strongly connected with the entanglement of the state corresponding to the negative eigenvalue of K(T) or the negative entropy of K.
From entanglement to discord: a perspective based on partial transposition
Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices
Robustness of entangled states that are positive under partial transposition
