Local Convertibility in quantum spin systems

TL;DR

This paper investigates local convertibility in quantum spin systems, linking it to quantum phases, entanglement, and symmetry breaking, and demonstrating its ability to detect global properties from small subsystems.

Contribution

It introduces the concept of differential local convertibility in quantum phases and connects it to long-range entanglement, topological order, and symmetry breaking.

Findings

dLC signals higher computational power in quantum phases

dLC can detect global properties from small subsystems

States with finite order parameters are locally convertible

Abstract

Local Convertibility refers to the possibility of transforming a given state into a target one, just by means of LOCC with respect to a given bipartition of the system and it is possible if and only if all the Renyi-entropies of the initial state are smaller than those of the target state. We apply this concept to adiabatic evolutions and ask whether they can be rendered through LOCC in the sense above. We argue that a lack of differential local convertibility (dLC) signals a higher computational power of the system's quantum phase, which is also usually connected with the existence of long-range entanglement, topological order, or edge-states. Remarkably, dLC can detect these global properties already by considering small subsystems. Moreover, we connect dLC to spontaneous symmetry breaking by arguing that states with finite order parameters must be the most classical ones and thus be locally convertible.