Efficient estimation of multipartite quantum coherence
Qi-Ming Ding, Xiao‐Xu Fang, Xiao Yuan, Ting Zhang, He Lu
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 multiqubit entangled states, including the Greenberger-Horne-Zeilinger state, the cluster state, and the W state, and show how their coherences are efficiently inferred from measuring a few observables.