Bounds on the multipartite entanglement of superpositions

TL;DR

This paper establishes bounds on the multipartite entanglement of superposition states using geometric and q-squashed measures, aiding in estimating entanglement and revealing that high fidelity states can differ significantly in entanglement.

Contribution

It provides the first bounds on multipartite entanglement of superpositions using geometric and q-squashed measures, enhancing entanglement estimation methods.

Findings

Bounds on entanglement of superpositions derived

High fidelity states can have different entanglement levels

Estimates aid in quantifying multipartite entanglement

Abstract

We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.