Real randomized measurements for analyzing properties of quantum states

TL;DR

This paper introduces simplified randomized measurement protocols, RRMs and PRRMs, that reduce complexity by limiting rotations, enabling efficient analysis of quantum states for tasks like entanglement characterization and property prediction.

Contribution

The paper presents two new randomized measurement methods that simplify implementation by restricting rotations, expanding practical tools for quantum state analysis.

Findings

RRMs and PRRMs effectively capture bipartite correlations.

These protocols facilitate high-dimensional entanglement characterization.

They enable quantum state property prediction with reduced complexity.

Abstract

Randomized measurements are useful for analyzing quantum systems especially when quantum control is not fully perfect. However, their practical realization typically requires multiple rotations in the complex space due to the adoption of random unitaries. Here, we introduce two simplified randomized measurements that limit rotations in a subspace of the complex space. The first is \textit{real randomized measurements} (RRMs) with orthogonal evolution and real local observables. The second is \textit{partial real randomized measurements} (PRRMs) with orthogonal evolution and imaginary local observables. We show that these measurement protocols exhibit different abilities in capturing correlations of bipartite systems. We explore various applications of RRMs and PRRMs in different quantum information tasks such as characterizing high-dimensional entanglement, quantum imaginarity, and predicting properties of quantum states with classical shadow.