A new entanglement measure based on the total concurrence

TL;DR

This paper introduces a new entanglement measure called total concurrence, derived from the dual form of q-concurrence, providing analytical bounds and expressions for specific states, and exploring its monogamy relations in qubit systems.

Contribution

It proposes the total concurrence as a new entanglement measure and derives analytical bounds, expressions, and monogamy relations for it in various quantum states.

Findings

Analytical lower bounds for the total concurrence.

Explicit formulas for isotropic and Werner states.

Monogamy relations for qubit systems.

Abstract

Quantum entanglement is a crucial resource in quantum information processing, advancing quantum technologies. The greater the uncertainty in subsystems' pure states, the stronger the quantum entanglement between them. From the dual form of $q$-concurrence ($q\geq 2$) we introduce the total concurrence. A bona fide measure of quantum entanglement is introduced, the $\mathcal{C}^{t}_q$-concurrence ($q \geq 2$), which is based on the total concurrence. Analytical lower bounds for the $\mathcal{C}^{t}_q$-concurrence are derived. In addition, an analytical expression is derived for the $\mathcal{C}^{t}_q$-concurrence in the cases of isotropic and Werner states. Furthermore, the monogamy relations that the $\mathcal{C}^{t}_q$-concurrence satisfies for qubit systems are examined. Additionally, based on the parameterized $\alpha$-concurrence and its complementary dual, the $\mathcal{C}^{t}_\alpha$-concurrence $(0\leq\alpha\leq\frac{1}{2})$ is also proposed.