Entanglement optimizing mixtures of two-qubit states

TL;DR

This paper investigates the conditions under which mixtures of two-qubit pure states maximize entanglement, revealing that optimal mixtures are rare for multiple states and exploring implications for superposition and rebit concurrence.

Contribution

It characterizes when mixtures of two-qubit pure states are optimal for entanglement, providing new conditions and showing limitations for larger sets of states.

Findings

28.5% of two-state mixtures are optimal

5.12% of three-state mixtures are optimal

No optimal sets exist for four or more states

Abstract

Entanglement in incoherent mixtures of pure states of two qubits is considered via the concurrence measure. A set of pure states is optimal if the concurrence for any mixture of them is the weighted sum of the concurrences of the generating states. When two or three pure real states are mixed it is shown that 28.5% and 5.12% of the cases respectively, are optimal. Conditions that are obeyed by the pure states generating such optimally entangled mixtures are derived. For four or more pure states it is shown that there are no such sets of real states. The implications of these on superposition of two or more dimerized states is discussed. A corollary of these results also show in how many cases rebit concurrence can be the same as that of qubit concurrence.