Maximally genuine multipartite entangled mixed X-states of N-qubits

TL;DR

This paper constructs N-qubit X-states with maximal genuine multipartite entanglement for any spectrum, optimizing entanglement measures and providing methods for state transformation and characterization.

Contribution

It introduces a method to generate maximally entangled X-states for any spectrum and develops a numerical strategy for quantum state transformations.

Findings

Maximal GM-concurrence X-states characterized for all spectra

Semidefinite programming used to find X-states with maximal entanglement for given purity

Efficient quantum operations designed for state transformations

Abstract

For every possible spectrum of $2^N$-dimensional density operators, we construct an $N$-qubit X-state of same spectrum and maximal genuine multipartite (GM-) concurrence, hence characterizing a global unitary transformation that --- constrained to output X-states --- maximizes the GM-concurrence of an arbitrary input mixed state of $N$ qubits. We also apply semidefinite programming methods to obtain $N$-qubit X-states with maximal GM-concurrence for a given purity and to provide an alternative proof of optimality of a recently proposed set of density matrices for the role, the so-called X-MEMS. Furthermore, we introduce a numerical strategy to tailor a quantum operation that converts between any two given density matrices using a relatively small number of Kraus operators. We apply our strategy to design short operator-sum representations for the transformation between any given $N$-qubit mixed state and a corresponding X-MEMS of same purity.