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arXiv · 1407.3021

Entanglement universality of two-qubit X-states

Paulo E. M. F. Mendonca·Marcelo A. Marchiolli·Diógenes Galetti
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Abstract

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.

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Paulo E. M. F. Mendonca, Marcelo A. Marchiolli, Diógenes Galetti. 2014-09-05. Entanglement universality of two-qubit X-states. https://doi.org/10.1016/j.aop.2014.08.017

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