Efficient estimation of multipartite quantum coherence

TL;DR

This paper introduces a method to efficiently estimate bounds of quantum coherence in large multipartite systems using minimal measurements, verified experimentally on four-qubit states.

Contribution

It presents a systematic approach for estimating coherence bounds in multipartite states with few measurements, leveraging stabilizer formalism and spectrum estimation.

Findings

Lower and upper bounds of coherence can be estimated with minimal measurements.

Experimental verification on four-qubit states demonstrates efficiency.

Method applies to various entangled states like GHZ, cluster, and W states.

Abstract

Quantification of coherence lies at the heart of quantum information processing and fundamental physics. Exact evaluation of coherence measures generally needs a full reconstruction of the density matrix, which becomes intractable for large-scale multipartite systems. Here, we propose a systematic theoretical approach to efficiently estimating lower and upper bounds of coherence in multipartite states. Under the stabilizer formalism, the lower bound is determined by the spectrum estimation method with a small number of measurements and the upper bound is determined by a single measurement. We verify our theory with a four-qubit optical quantum system.We experimentally implement various multi-qubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherence are efficiently inferred from measuring few observables.