Efficient estimation of multipartite quantum coherence
Qi-Ming Ding, Xiao‐Xu Fang, Xiao Hui Yuan, Ting Zhang, He Lu · Physical Review Research · 2021
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.