Tight bounds on the concurrence of quantum superpositions

TL;DR

This paper investigates how the entanglement, measured by concurrence, of superposed quantum states relates to their components, providing bounds and exact formulas, especially for bipartite pure states.

Contribution

It derives simple inequalities and exact expressions for the concurrence of superpositions, improving bounds and offering new insights into quantum entanglement.

Findings

Exact concurrence formula for biorthogonal states

Tighter upper bounds for qubits compared to previous work

General bounds applicable to all bipartite pure states

Abstract

The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we find simple inequalities relating the concurrence of the state to that of its components. We derive an exact expression for the concurrence when the component states are biorthogonal, and provide elegant upper and lower bounds in all other cases. For quantum bits, our upper bound is tighter than the previously derived bound in [Phys. Rev. Lett. 97, 100502 (2006).]