Entanglement of subspaces in terms of entanglement of superpositions

TL;DR

This paper explores bounds on the entanglement entropy of superpositions of bipartite states, extending previous results to multiple states and analyzing entanglement in subspaces with various measures.

Contribution

It generalizes bounds on entanglement of superpositions to multiple states and investigates entanglement bounds within subspaces using different measures.

Findings

Upper bounds for entanglement in subspaces

No lower bounds for minimal entanglement in subspaces

Extension of previous superposition entanglement results

Abstract

We investigate upper and lower bounds on the entropy of entanglement of a superposition of bipartite states as a function of the individual states in the superposition. In particular, we extend the results in [G. Gour, arxiv.org:0704.1521 (2007)] to superpositions of several states rather than just two. We then investigate the entanglement in a subspace as a function of its basis states: we find upper bounds for the largest entanglement in a subspace and demonstrate that no such lower bound for the smallest entanglement exists. Finally, we consider entanglement of superpositions using measures of entanglement other than the entropy of entanglement.