Detecting metrologically useful entanglement in the vicinity of Dicke states

Abstract

We present a method to verify the metrological usefulness of noisy Dicke states of a particle ensemble with only a few collective measurements, without the need for a direct measurement of the sensitivity. Our method determines the usefulness of the state for the usual protocol for estimating the angle of rotation with Dicke states, which is based on the measurement of the second moment of a total spin component. It can also be used to detect entangled states that are useful for quantum metrology. We test our approach on recent experimental results.

17 pages including 4 figures; v2: Sec. IV with further numerical examples added, Appendix added; v3: published version

References in corpus (19)

• 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
• Quantum limits in optical interferometry
• Twin matter waves for interferometry beyond the classical limit
• 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
• Multipartite entanglement in spin chains
• Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement
• Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
• Generation of macroscopic singlet states in a cold atomic ensemble
• Squeezed-light-enhanced atom interferometry below the standard quantum limit
• Practical methods for witnessing genuine multi-qubit entanglement in the vicinity of symmetric states
• Heisenberg-limited metrology with information recycling

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