Bounds of concurrence and their relation with fidelity and frontier states

TL;DR

This paper establishes bounds on quantum concurrence using fidelity properties and analytically characterizes states that achieve these bounds in two-qubit systems, enhancing understanding of entanglement measures.

Contribution

It provides a rigorous proof of concurrence bounds based on fidelity and analytically identifies states that attain these bounds in two-qubit systems.

Findings

Bounds of concurrence are proved using fidelity properties.

States achieving bounds are analytically determined for two-qubit systems.

The relationship between concurrence, fidelity, and frontier states is clarified.

Abstract

The bounds of concurrence in [F. Mintert and A. Buchleitner, Phys. Rev. Lett. 98 (2007) 140505] and [C. Zhang \textit{et. al.}, Phys. Rev. A 78 (2008) 042308] are proved by using two properties of the fidelity. In two-qubit systems, for a given value of concurrence, the states achieving the maximal upper bound, the minimal lower bound or the maximal difference upper-lower bound are determined analytically.