Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles

Abstract

We present a method to detect bipartite entanglement based on number-phase-like uncertainty relations in split spin ensembles. First, we derive an uncertainty relation that plays the role of a number-phase uncertainty for spin systems. It is important that the relation is given with well-defined and easily measurable quantities, and that it does not need assuming infinite dimensional systems. Based on this uncertainty relation, we show how to detect bipartite entanglement in an unpolarized Dicke state of many spin-1/2 particles. The particles are split into two subensembles, then collective angular momentum measurements are carried out locally on the two parts. First, we present a bipartite Einstein-Podolsky-Rosen (EPR) steering criterion. Then, we present an entanglement condition that can detect bipartite entanglement in such systems. We demonstrate the utility of the criteria by applying them to a recent experiment given in K. Lange et al. [Science 360, 416 (2018)] realizing a Dicke state in a Bose-Einstein condensate of cold atoms, in which the two subensembles were spatially separated from each other. Our methods also work well if split spin-squeezed states are considered. We show in a comprehensive way how to handle experimental imperfections, such as the nonzero particle number variance including the partition noise, and the fact that, while ideally BECs occupy a single spatial mode, in practice the population of other spatial modes cannot be fully suppressed.

34 pages including 5 figures, quantumarticle

References in corpus (29)

• Entanglement detection
• Scalable multi-particle entanglement of trapped ions
• 14-qubit entanglement: creation and coherence
• Nonlinear atom interferometer surpasses classical precision limit
• Quantum metrology from a quantum information science perspective
• Squeezing and entanglement in a Bose-Einstein condensate
• Experimental entanglement of six photons in graph states
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Twin matter waves for interferometry beyond the classical limit
• Entanglement Certification $-$ From Theory to Experiment
• Experimental entanglement of a six-photon symmetric Dicke state
• Experimental Observation of Four-Photon Entangled Dicke State with High Fidelity
• Scalable Spin Squeezing for Quantum-Enhanced Magnetometry with Bose-Einstein Condensates
• Detecting multiparticle entanglement of Dicke states
• Characterizing the entanglement of symmetric many-particle spin-1/2 systems
• Spin squeezing and entanglement
• Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement
• Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
• Quantum entanglement of a large number of photons
• Measures of macroscopicity for quantum spin systems
• Energy as an Entanglement Witness for Quantum Many-Body Systems
• EPR entanglement strategies in two-well BEC
• Entanglement Detection in Optical Lattices of Bosonic Atoms with Collective Measurements
• Quantum Metrology with Dicke Squeezed States
• Entanglement Detection Based on Interference and Particle Counting
• Entanglement and Extreme Spin Squeezing for a Fluctuating Number of Indistinguishable Particles
• Entanglement quantification in atomic ensembles
• Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
• Uncertainty relations for the realisation of macroscopic quantum superpositions and EPR paradoxes

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• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Assisted metrology and preparation of macroscopic superpositions with split spin-squeezed states
• Degrees of Entanglement in Systems of Three Indistinguishable Bosons: Revisiting the Greenberger-Horne-Zeilinge State