An explicit formula for the polynomial entanglement measures of degree 2 of even-N qubits mixed states

TL;DR

This paper derives an explicit formula for degree-2 polynomial entanglement measures of even-N qubits mixed states, simplifying the quantification of multipartite entanglement similar to Wooters' formula.

Contribution

It provides a novel explicit formula for degree-2 polynomial entanglement measures of even-N qubits mixed states, extending entanglement quantification methods.

Findings

The formula is similar to Wooters' formula for bipartite entanglement.

The formula applies to X density matrices and aligns with GM entanglement.

Results simplify entanglement measurement for specific multipartite states.

Abstract

Characterization of the multipartite mixed state entanglement is still a challenging problem. Since due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state \r{ho} of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this Letter, we give an explicit formula for the polynomial entanglement measures of degree 2 of even-N qubits mixed states that is similar to Wooters formula in [1]. Then we discuss our findings in the framework of X density matrices and show that our formula for this type of density matrices is in the full agreement with the genuine multipartite (GM) entanglement of these states.