Many experiments in quantum information aim at creating graph states. Quantifying the purity of an experimentally achieved graph state could in principle be accomplished using full-state tomography. This method requires a number of measurement settings growing exponentially with the number of constituents involved. Thus, full-state tomography becomes experimentally infeasible even for a moderate number of qubits.
In this paper we present a method to estimate the purity of experimentally achieved graph states with simple measurements. The observables we consider are the stabilizers of the underlying graph. Then, we formulate the problem as: "What is the state with the least purity that is compatible with the measurement data?" We solve this problem analytically and compare the obtained bounds with results from full-state tomography for simulated data.
An Algorithm for Estimating $α$-Stabilizer Rényi Entropies via Purity
Quantum Engineering Centre for Doctoral Training, H. H. Wills Physics Laboratory and Department of Electrical & Electronic Engineering, University of Bristol（量子工程博士培训中心，H.H.威尔斯物理实验室和电气与电子工程系，布里斯托大学）；H.H. Wills Physics Laboratory, University of Bristol（H.H.威尔斯物理实验室，布里斯托大学）
Reduced-State Stabilizer Rényi Entropy as a Probe of Quantum Criticality in the Transverse ANNNI Model and the Quantum Compass Model
National Institute of Technology Sikkim（锡金国家技术学院）；Tamkang University（淡江大学）；Hon Hai Research Institute（鸿海研究院）；National Center for Theoretical Sciences（国家理论科学中心）
We propose a method to calculate the purity of reduced states of graph states entirely within the stabilizer formalism, using only the stabilizer generators for a given state. We apply this method to find the Concentratable Entanglement of graph states, with examples including a single qubit within any graph state, states proposed for use in quantum repeaters and states that maximise and minimise the overall Concentratable Entanglement.
Reduced State Stabilizer Rényi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models
Tamkang University（淡江大学）；National Institute of Technology Sikkim（锡金国立技术学院）；Hon Hai Research Institute（鸿海研究院）；National Center for Theoretical Sciences（国家理论科学中心）
Van Hove singularities in stabilizer entropy densities
Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
Qurrium: A Python package for randomized measurement-based estimation of quantum state properties
Academia Sinica（中央研究院）；National Chengchi University（国立政治大学）；National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Quantum Machines, Singapore（新加坡量子机器公司）
