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arXiv · 1612.01214

Maximally entangled mixed states for qubit-qutrit systems

Paulo E. M. F. Mendonca·Marcelo A. Marchiolli·Samuel R. Hedemann
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Abstract

We consider the problems of maximizing the entanglement negativity of X-form qubit-qutrit density matrices with (i) a fixed spectrum and (ii) a fixed purity. In the first case, the problem is solved in full generality whereas, in the latter, partial solutions are obtained by imposing extra spectral constraints such as rank-deficiency and degeneracy, which enable a semidefinite programming treatment for the optimization problem at hand. Despite the technically-motivated assumptions, we provide strong numerical evidence that three-fold degenerate X states of purity $P$ reach the highest entanglement negativity accessible to arbitrary qubit-qutrit density matrices of the same purity, hence characterizing a sparse family of likely qubit-qutrit maximally entangled mixed states.

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Paulo E. M. F. Mendonca, Marcelo A. Marchiolli, Samuel R. Hedemann. 2016-12-05. Maximally entangled mixed states for qubit-qutrit systems. https://doi.org/10.1103/physreva.95.022324

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