Error estimation of different schemes to measure spin-squeezing inequalities

Abstract

How can we analyze quantum correlations in large and noisy systems without quantum state tomography? An established method is to measure total angular momenta and employ the so-called spin-squeezing inequalities based on their expectations and variances. This allows detection of metrologically useful entanglement, but efficient strategies for estimating such nonlinear quantities have yet to be determined. In this paper we show that spin-squeezing inequalities can not only be evaluated by measurements of the total angular momentum but also by two-qubit correlations, either involving all pair correlations or randomly chosen pair correlations. Then we analyze the estimation errors of our approaches in terms of a hypothesis test. For this purpose, we discuss how error bounds can be derived for nonlinear estimators with the help of their variances, characterizing the probability of falsely detecting a separable state as entangled. We focus on the spin-squeezing inequalities in multiqubit systems. Our methods, however, can also be applied to spin-squeezing inequalities for qudits or for the statistical treatment of other nonlinear parameters of quantum states.

22 pages, 9 figures

References in corpus (34)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Entanglement detection
• Trapped-Ion Quantum Computing: Progress and Challenges
• Quantum interface between light and atomic ensembles
• Experimental long-lived entanglement of two macroscopic objects
• Many-particle entanglement with Bose--Einstein condensates
• Atom chip based generation of entanglement for quantum metrology
• Quantum spin squeezing
• Quantum metrology from a quantum information science perspective
• Squeezing and entanglement in a Bose-Einstein condensate
• Direct Fidelity Estimation from Few Pauli Measurements
• Quantum noise limited and entanglement-assisted magnetometry
• Entanglement Certification $-$ From Theory to Experiment
• Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
• Optimal spin squeezing inequalities detect bound entanglement in spin models
• Spin squeezing and entanglement
• Bell Correlations in a Bose-Einstein Condensate
• Quantum metrology with a scanning probe atom interferometer
• Spin squeezing inequalities and entanglement of $N$ qubit states
• Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement
• Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Measurement-induced nonlocal entanglement in a hot, strongly-interacting atomic system
• Generalized spin squeezing inequalities in $N$ qubit systems: theory and experiment
• A trapped-ion based quantum byte with $10^{-5}$ next-neighbour cross-talk
• Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
• Spin Squeezing by Rydberg Dressing in an Array of Atomic Ensembles
• Statistical Methods for Quantum State Verification and Fidelity Estimation
• Single-copy entanglement detection
• Experimental Realization of the Rabi-Hubbard Model with Trapped Ions
• Experimental few-copy multi-particle entanglement detection
• Entanglement quantification in atomic ensembles
• Inter-species spin-noise correlations in hot atomic vapors
• Multi-partite entanglement detection with non symmetric probing