A new parameterized entanglement monotone

TL;DR

This paper introduces a new parameterized entanglement monotone called q-concurrence, derived from Tsallis entropy, with analytical bounds and computational methods, advancing the understanding of bipartite entanglement in quantum information.

Contribution

It proposes the q-concurrence as a novel entanglement measure, derives bounds using separability criteria, and develops a computational approach for estimation.

Findings

Derived analytical lower bounds for q-concurrence.

Characterized bipartite isotropic states using q-concurrence.

Superposition can increase q-concurrence up to one ebit.

Abstract

Entanglement concurrence has been widely used for featuring entanglement in quantum experiments. As an entanglement monotone it is related to specific quantum Tsallis entropy. Our goal in this paper is to propose a new parameterized bipartite entanglement monotone which is named as $q$-concurrence inspired by general Tsallis entropy. We derive an analytical lower bound for the $q$-concurrence of any bipartite quantum entanglement state by employing positive partial transposition criterion and realignment criterion, which shows an interesting relationship to the strong separability criteria. The new entanglement monotone is used to characterize bipartite isotropic states. Finally, we provide a computational method to estimate the $q$-concurrence for any entanglement by superposing two bipartite pure states. It shows that the superposition operations can at most increase one ebit for the $q$-concurrence in the case that the two states being superposed are bi-orthogonal or one-sided orthogonal. These results reveal a series of new phenomena about the entanglement, which may be interesting in quantum communication and quantum information processing.