Quantum coherences, K -way negativities and multipartite entanglement
S. Shelly Sharma, Naresh Kumar Sharma · Physical Review A · 2008
A characterization of multipartite quantum states having $N$ subsystems, based on negativities of matrices obtained by selective partial transposition of the state operator, is proposed. The $K$-way partial transpose with respect to a subsystem is constructed by imposing constraints involving the states of $K$ subsystems of the multipartite composite system. The $K$-way negativity, defined as the negativity of $K$-way partial transpose, quantifies the $K$-way coherences of the composite system. For an $N$-partite system the fraction of $K$-way negativity $(2\ensuremath{\le}K\ensuremath{\le}N)$, contributing to global negativity, is obtained. The entanglement measures for a given state $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\rho}}$ are identified as the partial $K$-way negativities of the corresponding canonical state.