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arXiv:1410.5353 · Nature Communications

Joint estimation of phase and phase diffusion for quantum metrology

Mihai D. Vidrighin, Gaia Donati, Marco G. Genoni, Xian‐Min Jin, W. Steven Kolthammer, Myungshik Kim, Animesh Datta, Marco Barbieri, Ian A. Walmsley

Published Apr 14, 2014• 217 citations
arXivHTMLPDF
DOI
10.1038/ncomms4532

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Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase and phase diffusion has emerged as an effective approach, transforming the problem into a multi-parameter estimation task. However, the incompatibility between optimal measurements for different parameters prevents single-copy measurements from reaching the fundamental precision limits defined by the quantum Cramer-Rao bound. Meanwhile, collective measurements performed on multiple identical copies can mitigate this incompatibility and thus enhance the precision of joint parameter estimation. This work experimentally demonstrates joint phase and phase-diffusion estimation using deterministic Bell measurements on a two-qubit system. A linear optical network is employed to implement both parameter encoding and deterministic Bell measurements, achieving improved estimation precision compared to any separable measurement strategy. This work proposes a new framework for phase estimation under phase-diffusive noise and underscores the substantial advantages of collective measurements in multi-parameter quantum metrology.
Abstract Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.
This thesis explores the field of optomechanics and the theory of multi-parameter estimation for quantum metrology applications. An optomechanical state inside a microresonator-taper system is studied experimentally, where the optical and mechanical modes interact by means of Brillouin anti-Stokes scattering. The scattering leads to sideband cooling of the mechanical (acoustic) mode and the underlying optomechanical coupling takes the form of a beam-splitter interaction Hamiltonian. The mechanical mode is further cooled by continuously monitoring the optical anti-Stokes mode by a heterodyne detector. The resulting time-domain data is input offline to a stochastic master equation model for Gaussian states to optimally estimate the mechanical phase space trajectories and subsequently reduce the observer’s uncertainty associated with the phase space coordinates. It is shown that more information about the mechanical mode can be obtained by heterodyne monitoring than by the commonly used in optomechanics homodyne detection for the beam-splitter type interaction Hamiltonians. The second part of this thesis theoretically considers the problem of simultaneous estimation of phase and phase diffusion using fixed-particle number states in the framework of quantum Cramér-Rao bound. Quantum Fisher information matrices are derived analytically in the limits of large and small diffusive noise to quantify the maximum amount of information available in the individual estimation of the parameters. The former is for a general fixed-particle number state and the latter for Holland-Burnett states for which quantum-enhanced estimation of phase as well as diffusion can be obtained. The precision limits given by quantum Fisher information may not be achievable in the joint estimation of the parameters due to the possible non-commutativity of the optimal measurements and this can be quantified in terms of a trade-off relation. This trade-off relation can reach the maximum of 2 in the large diffusion regime, whereas in the small diffusion regime a numerical evidence is shown that the optimal trade-off relation approaches 1 for Holland-Burnett states. These numerical results are valid in the small particle number regime. Finally, numerical results showing behaviour of the trade-off for a general value of phase diffusion when using Holland-Burnett states are provided.