Complete characterization of quantum correlations by randomized measurements

TL;DR

This paper introduces a method using randomized measurements to directly characterize quantum correlations in experiments, simplifying analysis without shared reference frames, and demonstrates its application on entangled photon pairs.

Contribution

It provides a novel approach to measure locally invariant quantum properties directly via randomized measurements, facilitating experimental analysis of quantum correlations.

Findings

Successfully implemented on entangled photons

Characterized quantum teleportation usefulness

Potential to reveal quantum nonlocality

Abstract

The fact that quantum mechanics predicts stronger correlations than classical physics is an essential cornerstone of quantum information processing. Indeed, these quantum correlations are a valuable resource for various tasks, such as quantum key distribution or quantum teleportation, but characterizing these correlations in an experimental setting is a formidable task, especially in scenarios where no shared reference frames are available. By definition, quantum correlations are reference-frame independent, i.e., invariant under local transformations; this physically motivated invariance implies, however, a dedicated mathematical structure and, therefore, constitutes a roadblock for an efficient analysis of these correlations in experiments. Here we provide a method to directly measure any locally invariant property of quantum states using locally randomized measurements, and we present a detailed toolbox to analyze these correlations for two quantum bits. We implement these methods experimentally using pairs of entangled photons, characterizing their usefulness for quantum teleportation and their potential to display quantum nonlocality in its simplest form. Our results can be applied to various quantum computing platforms, allowing simple analysis of correlations between arbitrary distant qubits in the architecture.