Maximally entangled mixed states for qubit-qutrit systems

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...

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Bibliographic Details
Published in:arXiv.org 2016-12
Main Authors: Paulo E M F Mendonca, Marchiolli, Marcelo A, Hedemann, Samuel R
Format: Article
Language:English
Subjects:
Density
Optimization
Purity
Quantum entanglement
Semidefinite programming
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1612.01214