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Laser Physics Letters

High precision regions of phase sensitivity for the superposition of coherent fields

K. Berrada

Published Sep 1, 2014• 10 citations
Publisher

Abstract

We investigate the problem of parameter estimation for the superposition of coherent fields under perfect and lossy regimes. We show the optimal range for higher precision of phase estimation by exactly solving a model consisting of a Schrödinger-cat state (SCS) subject to zero-temperature under a decoherence effect due to a dissipative interaction with an environment. We find the phenomenon that the quantum Fisher information (QFI), namely, the precision of estimation, is slowly reduced with the environment effect and affected by the photon number effects. We find that revivals and retardation of the QFI loss may occur by adjusting the mean photon number, and increasing the photons strongly enhances the coherence and hence augments the resolution of the parameter estimation. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the coherent field and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the mean photon number. These features make the SCS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.

DOI
10.1088/1612-2011/11/10/105202

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Abstract We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
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We extend our previous study of squeezed two-component Schrödinger cat states to a phase-referenced single-mode family with an arbitrary number NNN of coherent components and general relative phases. Within the established circular-state construction, we derive a closed complex overlap kernel for the ordered action of displacement, phase rotation, and squeezing, retaining exact finite-amplitude normalization. We distinguish finite-displacement orthogonality from local phase-estimation sensitivity quantified by quantum Fisher information (QFI). For equal-phase states, we compare N=2,…,9N=2,\ldots,9N=2,…,9 at a common mean photon number and include coherent-state and squeezed-vacuum benchmarks. A bound on the higher photon-number sectors establishes the fixed-energy asymptote FQ,N=4nˉ(N−nˉ)+o(1)F_{Q,N}=4\bar n(N-\bar n)+o(1)FQ,N​=4nˉ(N−nˉ)+o(1). Its leading term agrees with the known QFI of a vacuum--NNN-photon superposition. The resulting decrease of the ideal local quantum Cramér--Rao bound does not establish unlimited attainable precision: prior phase information, sample size, phase-reference resources, optical loss, state preparation, and measurement choice remain relevant.
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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.
We investigate the performance of entangled coherent states for quantum-enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.