Nondestructive Verification of Entangled States via Fidelity Witnessing

TL;DR

This paper introduces nondestructive methods for verifying the fidelity of entangled states, enabling efficient distinction between states above or below a fidelity threshold without destroying the states.

Contribution

It proposes novel fidelity witnessing techniques that are more efficient and preserve the states, outperforming traditional measurement methods for certain state families.

Findings

Methods can distinguish states above or below fidelity thresholds efficiently

Approaches outperform direct measurement methods for specific state families

Verification preserves the entangled states for further use

Abstract

Assessing the quality of an ensemble of noisy entangled states is a central task in quantum information processing. Usually this is done by measuring and hence destroying multiple copies, from which state tomography or fidelity estimation can be employed to characterize states. Here we propose several methods to directly distinguish between two different sets of states, e.g. if their fidelity is above or below a certain threshold value. This turns out to be significantly more efficient, and importantly keeps the verified states intact. We make use of auxiliary entanglement or an ensemble of larger size, where we operate on the whole ensemble, but measure only a small fraction where information has been concentrated. For certain state families, we demonstrate that such an approach can even outperform optimal methods that collectively measure directly a fixed fraction of the ensemble.