On the concurrence of superpositions of many states

TL;DR

This paper investigates bounds on the entanglement of superpositions of bipartite states using the concurrence vector, providing tighter bounds especially for orthogonal states and extending to multiple states.

Contribution

It establishes that the concurrence vector matches I-concurrence and derives tighter bounds on entanglement for superpositions, including multiple states.

Findings

Tighter lower bounds for orthogonal superposed states.

Bounds are generally tighter than previous I-concurrence-based bounds.

Extension of bounds to superpositions of more than two states.

Abstract

In this paper we use the \textit{concurrence vector}, as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by \textit{I-concurrence}, so that our results can be compared to those given in [Phys. Rev. A {\bf 76}, 042328 (2007)]. We obtain a tighter lower bound in the case that two superposed states are orthogonal. We also show that when the two superposed states are not necessarily orthogonal, both lower and bounds are, in general, tighter than the bounds given in terms of the I-concurrence. An extension of the results to the case with more than two states in the superpositions is also given.