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arXiv:2110.12548 · The European Physical Journal Plus

Quantum phase estimations with spin coherent states superposition

Yusef Maleki

Published Oct 1, 2021• 12 citations
arXivHTMLPDF
DOI
10.1140/epjp/s13360-021-02020-8

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We present a closed-form analytical description for the metrological performance of a generic superposition of spin coherent states (SSCS) used as probes for quantum phase estimation. Working in this framework, we derive transparent analytical expressions for the pertinent quantum Fisher information and identify a general class of spin coherent states enabling quantum metrology with Heisenberg-limit precision. Bloch-sphere analysis of antipodal SSCS shows that the phase-estimation precision attainable with such states increases with the distance from the equator of the Bloch sphere, growing from the shot-noise limit level for the equatorial states all the way up to the Heisenberg limit for SSCS that can be represented as superpositions of the poles of the Bloch sphere.
Quantum metrology faces major challenges in noisy environments, where decoherence rapidly degrades useful quantum resources. We investigate the dynamics of the precision limits given by the quantum Fisher information (QFI) for phase estimation under spatially correlated dephasing. We characterize the dynamics of the QFI by the sensitivity and degradation indicators that can be obtained as analytical expressions derived using perturbative theory treatment. These short-time and weak-noise formulas yield analytic insight into how collective-spin moments govern both (i) the noiseless sensitivity and (ii) the leading noise-induced degradation of metrological usefulness. We identify a trade-off that is intrinsic to our commuting encoding-noise structure. We analyze the QFI dynamics for the Gaussian spin state (GSS) superpositions, encompassing spin coherent state (SCS), Dicke state superpositions, spin-squeezed states, and GHZ-like states. Predictions from indicators of the QFI dynamics are compared to both the quantum Cramér--Rao bound and the measurement-specific sensitivity bounds for an optimal parameter and interrogation time under a finite total time resource. When possible, we analytically derive the measurement-specific sensitivity bounds for spin-projection and parity-based measurements.