Reexamination of determinant-based separability test for two qubits

TL;DR

This paper reexamines a determinant-based test for entanglement in two-qubit states, clarifies its relation to concurrence, and explores entanglement monogamy and a related monotone.

Contribution

It clarifies the relationship between the pseudo entanglement monotone π and concurrence, and rephrases monogamy of entanglement in terms of π, including a proof of the factorization law.

Findings

π is closely related to concurrence through shared construction.

Monogamy of entanglement can be expressed using π.

The factorization law for π is proven.

Abstract

It was shown in [Augusiak et al.,\;Phys. Rev. A \textbf{77}, 030301(R) (2008)] that discrimination between entanglement and separability in a two qubit state can be achieved by a measurement of a single observable on four copies of it. Moreover, a pseudo entanglement monotone $\pi$ was proposed to quantify entanglement in such states. The main goal of the present paper is to show that close relationship between $\pi$ and concurrence reported there is a result of sharing the same underlying construction of a spin flipped matrix. We also show that monogamy of entanglement can be rephrased in terms of $\pi$ and prove the factorization law for $\pi$.