Reexamination of entanglement of superpositions

TL;DR

This paper derives tight bounds on the entanglement of superpositions of bipartite states, improving previous bounds and providing explicit formulas in special cases, advancing understanding of quantum entanglement properties.

Contribution

It introduces significantly tighter bounds on entanglement of superpositions and explicit formulas for orthogonal states, enhancing prior theoretical frameworks.

Findings

Tighter upper bounds on entanglement of superpositions.

Lower bounds applicable to various entanglement measures.

Explicit entanglement expressions for orthogonal superpositions.

Abstract

We find tight lower and upper bounds on the entanglement of a superposition of two bipartite states in terms of the entanglement of the two states constituting the superposition. Our upper bound is dramatically tighter than the one presented in Phys. Rev. Lett 97, 100502 (2006) and our lower bound can be used to provide lower bounds on different measures of entanglement such as the entanglement of formation and the entanglement of subspaces. We also find that in the case in which the two states are one-sided orthogonal, the entanglement of the superposition state can be expressed explicitly in terms of the entanglement of the two states in the superposition.