Maximally entangled mixed states for qubit-qutrit systems

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.

arXiv comment19 pages, 6 figures

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Cited by in corpus (11)

• Inertias of entanglement witnesses
• On the discrete Wigner function for SU(N)
• Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM quantum computer
• Maximum entanglement of mixed symmetric states under unitary transformations
• Bounds on bipartite entanglement from fixed marginals
• Extensions of Generalized Two-Qubit Separability Probability Analyses to Higher Dimensions, Additional Measures and New Methodologies
• Phase diagram for the one-way quantum deficit of two-qubit X states
• Master Lovas-Andai and Equivalent Formulas Verifying the $\frac{8}{33}$ Two-Qubit Hilbert-Schmidt Separability Probability and Companion Rational-Valued Conjectures
• Entanglement Universality of TGX States in Qubit-Qutrit Systems
• Multipartite Mixed Maximally Entangled States: Mixed States with Entanglement 1
• Representations of two-qubit and ququart states via discrete Wigner functions