Efficient estimation of multipartite quantum coherence

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.

13 pages, 8 figures. Comments are welcome

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Cited by in corpus (10)

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• Experimental quantum state measurement with classical shadows
• Quantification of Entanglement and Coherence with Purity Detection
• Maximal coin-position entanglement generation in a quantum walk for the third step and beyond regardless of the initial state
• No-go theorems for deterministic purification and probabilistic enhancement of coherence
• Experimental investigation of quantum uncertainty relations with classical shadows
• Experimental distillation of tripartite quantum steering with an optimal local filtering operation
• A Compendious Review of Majorization-Based Resource Theories: Quantum Information and Quantum Thermodynamics
• The tightness of multipartite coherence from spectrum estimation
• Scalable protocol to coherence estimation from scarce data: Theory and experiment