Entanglement Cost for Steering Assemblages

TL;DR

This paper investigates the quantification of entanglement needed to generate steering assemblages, extending entanglement measures and providing bounds and properties relevant for quantum information processing.

Contribution

It introduces entanglement cost and formation for steering assemblages, extending existing concepts and analyzing their properties and bounds through semidefinite programming.

Findings

Entanglement of formation for assemblages is not continuous.

It is not a flat roof extension.

Numerical analysis illustrates these properties.

Abstract

In this paper we pose the question of how one can quantify the amount of entanglement necessary to create a given steering assemblage, when the original state and measurements are unknown. To do this, we extend the concepts of entanglement cost and entanglement of formation to steering assemblages, and show how to upper bound them with semidefinite programming. We prove that the entanglement of formation for assemblages is not generally continuous and not a flat roof extension; and use numerical analysis to illustrate these properties. Finally, we discuss the consequences of these results for assemblage-to-assemblage conversion and directions for further research.