Collective randomized measurements in quantum information processing

TL;DR

This paper introduces collective randomized measurements using collective angular momentum to analyze quantum entanglement, providing new criteria that go beyond traditional spin-squeezing inequalities and enabling entanglement detection in spatially-separated ensembles.

Contribution

It proposes a novel collective measurement approach for quantum systems, extending randomized measurement techniques to collective observables and developing new entanglement criteria.

Findings

Accessible spin-squeezing inequalities in the collective measurement scenario

An entanglement criterion based on three-body correlations

Application to characterize entanglement between spatially-separated ensembles

Abstract

The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially-separated two ensembles.