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 threefold degenerate X states of purity 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.
- Received 4 December 2016
DOI:https://doi.org/10.1103/PhysRevA.95.022324
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