Characterizing correlation within multipartite quantum systems via local randomized measurements

TL;DR

This paper introduces an experimentally feasible method to quantify total correlations in multipartite quantum systems using only single-qubit measurements, avoiding complex tomography.

Contribution

It presents a new correlation measure that is easier to estimate experimentally, enabling analysis of multipartite correlations in near-term quantum devices.

Findings

The proposed measure requires fewer measurements than tomography.

It can be estimated with only local single-qubit measurements.

The method is suitable for implementation on near-term quantum hardware.

Abstract

Given a quantum system on many qubits split into a few different parties, how many total correlations are there between these parties? Such a quantity, aimed to measure the deviation of the global quantum state from an uncorrelated state with the same local statistics, plays an important role in understanding multipartite correlations within complex networks of quantum states. Yet, the experimental access of this quantity remains challenging as it tends to be non-linear, and hence often requires tomography which becomes quickly intractable as dimensions of relevant quantum systems scale. Here, we introduce a much more experimentally accessible quantifier of total correlations, which can be estimated using only single-qubit measurements. It requires far fewer measurements than state tomography and obviates the need to coherently interfere multiple copies of a given state. Thus, we provide a tool for proving multipartite correlations that can be applied to near-term quantum devices.