Entanglement cost in practical scenarios

TL;DR

This paper investigates the one-shot entanglement cost for bipartite states in practical finite-resource scenarios, revealing a fundamental link between Schmidt number and entanglement of formation, and generalizing traditional entanglement cost expressions.

Contribution

It introduces a finite-resource, approximate framework for entanglement cost and uncovers a key relation between Schmidt number and entanglement of formation.

Findings

Derived a formula for one-shot entanglement cost in practical scenarios.

Established a fundamental relation between Schmidt number and entanglement of formation.

Reproduced the standard entanglement cost expression as a special case.

Abstract

We quantify the one-shot entanglement cost of an arbitrary bipartite state, that is the minimum number of singlets needed by two distant parties to create a single copy of the state up to a finite accuracy, using local operations and classical communication only. This analysis, in contrast to the traditional one, pertains to scenarios of practical relevance, in which resources are finite and transformations can only be achieved approximately. Moreover, it unveils a fundamental relation between two well-known entanglement measures, namely, the Schmidt number and the entanglement of formation. Using this relation, we are able to recover the usual expression of the entanglement cost as a special case.