2014/07/31 by Paulo E. M. F. Mendonca, Marcelo A. Marchiolli, Diógenes Galetti · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1016/j.aop.2014.08.017
published as Annals of Physics 351 (2014) 79 - 103 · 24 pages, 6 figures. v2 includes new references and minor changes (accepted version)
arxiv created 2014/09/05 · arxiv updated 2014/09/18
We demonstrate that for every two-qubit state there is a X-counterpart, i.e., a corresponding two-qubit X-state of same spectrum and entanglement, as measured by concurrence, negativity or relative entropy of entanglement. By parametrizing the set of two-qubit X-states and a family of unitary transformations that preserve the sparse structure of a two-qubit X-state density matrix, we obtain the parametric form of a unitary transformation that converts arbitrary two-qubit states into their X-counterparts. Moreover, we provide a semi-analytic prescription on how to set the parameters of this unitary transformation in order to preserve concurrence or negativity. We also explicitly construct a set of X-state density matrices, parametrized by their purity and concurrence, whose elements are in one-to-one correspondence with the points of the concurrence versus purity (CP) diagram for generic two-qubit states.