Entanglement monotones and transformations of symmetric bipartite states

TL;DR

This paper develops methods to compute entanglement monotones for symmetric bipartite states, enabling precise conditions for state transformations in quantum resource theories.

Contribution

It introduces a way to compute convex roofs of entanglement measures for Werner and isotropic states, and provides criteria for deterministic state conversions.

Findings

Closed-form convex roof calculations for Werner states.

Convex roof of Vidal monotones for isotropic states.

Necessary and sufficient conditions for state transformations.

Abstract

The primary goal in the study of entanglement as a resource theory is to find conditions that determine when one quantum state can or cannot be transformed into another via local operations and classical communication. This is typically done through entanglement monotones or conversion witnesses. Such quantities cannot be computed for arbitrary quantum states in general, but it is useful to consider classes of symmetric states for which closed-form expressions can be found. In this paper, we show how to compute the convex roof of any entanglement monotone for all Werner states. The convex roofs of the well-known Vidal monotones are computed for all isotropic states, and we show how this method can generalize to other entanglement measures and other types of symmetries as well. We also present necessary and sufficient conditions that determine when a pure bipartite state can be deterministically converted into a Werner state or an isotropic state.