Quantum Circuits assisted by LOCC: Transformations and Phases of Matter

TL;DR

This paper introduces protocols combining low-depth quantum circuits and LOCC to classify quantum phases and enhance unitary operations, revealing how complex entangled states can become trivial.

Contribution

It presents a novel framework for state transformations using low-depth circuits and LOCC, enabling phase classification and improved unitary operation capabilities.

Findings

Topologically-ordered states can be rendered trivial through the proposed protocols.

LOCC enhances the set of implementable unitary operations in quantum circuits.

The classification of quantum phases is extended via these transformation protocols.

Abstract

We introduce deterministic state-transformation protocols between many-body quantum states which can be implemented by low-depth Quantum Circuits (QC) followed by Local Operations and Classical Communication (LOCC). We show that this gives rise to a classification of phases in which topologically-ordered states or other paradigmatic entangled states become trivial. We also investigate how the set of unitary operations is enhanced by LOCC in this scenario, allowing one to perform certain large-depth QC in terms of low-depth ones.