I derive ultimate lower bound on the precision of polarization estimation for classical coherent light. I show that it is attainable with conventional detection schemes and discuss role of the global phase in this problem.
We study the limits that quantum mechanics imposes on the accuracy of the measurement of the Stokes polarization-vector in the case of classical states. Using the apparatus of the conventional Stokes receiver, we propose an estimation method that allows not only to exceed the signal-to-noise limit that is achieved by a heterodyne measurement or after ideal phase-insensitive amplification, but also to achieve the quantum SNR limit for the measurement of classical light. We refer to this receiver scheme as the enhanced Stokes receiver.
We present a comprehensive and pedagogical formulation of Bayesian multiparameter quantum estimation. Within this framework, we analyse the role of measurement incompatibility and establish its quantitative effect on attainable precision. We achieve this by deriving upper bounds based on the pretty good measurement -- a notion from hypothesis testing -- combined with the evaluation of the Nagaoka-Hayashi lower bound. In general, we prove that, as in the many-copy regime of local estimation theory, incompatibility can at most double the minimum loss relative to the idealised scenario in which individually optimal measurements are assumed jointly implementable. Therefore, in practical situations, the latter may provide a sufficient and computationally efficient benchmark without solving the full optimisation problem. Our results, which we illustrate through applications of discrete phase imaging, phase and dephasing estimation, and qubit sensing, provide analytical and numerical tools for assessing ultimate precision limits and the role of measurement incompatibility in Bayesian multiparameter quantum metrology, including an open-source package for all the bounds discussed here.
Multiparameter quantum metrology plays a fundamental role in uncovering and exploiting the distinctive features of quantum systems. In this work, we propose an effective and experimentally feasible scheme to significantly enhance the simultaneous quantum estimation of the photon magnon and magnon mechanical coupling strengths in a hybrid cavity magnon mechanical platform. Our approach relies on the assistance of a coherent feedback loop combined with the injection of a coherent driving field. We show that an appropriate tuning of the system and feedback parameters leads to a substantial reduction of the estimation errors associated with both coupling strengths. To quantify the metrological performance of the proposed scheme, we employ the quantum Cramer Rao bound (QCRB) as a fundamental benchmark for multiparameter estimation. We explicitly compute and compare the QCRBs derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) formalisms. Our results demonstrate that the RLD based QCRB is systematically lower than the SLD based bound, indicating superior estimation precision in the considered noncommutative estimation scenario. We further analyze the performance of heterodyne detection and show that, in suitable parameter regimes, the corresponding classical estimation precision closely approaches the ultimate quantum limit predicted by our scheme. Finally, we discuss the experimental feasibility of the proposed setup within currently available cavity magnon mechanical platforms. Owing to its general character, the framework developed here can be readily extended to the high precision estimation of other physical parameters in hybrid quantum systems.
Quantum phase measurement with multiphoton twin-Fock states has been shown to be optimal for detecting equal numbers of photons at the output ports of a Mach–Zehnder interferometer (i.e., the so-called single-fringe detection), since the phase sensitivity can saturate the quantum Cramér–Rao lower bound at certain values of phase shift. Here we report a further step to achieve a global phase estimation at the Heisenberg limit by detecting the particle-number difference (i.e., the J ^ z measurement). We show the role of experimental imperfections on the ultimate estimation precision with the six-photon twin-Fock state of light. Our results show that both the precision and the sensing region of the J ^ z measurement are better than those of the single-fringe detection, due to combined contributions of the measurement outcomes. We numerically simulate the phase estimation protocol using an asymptotically unbiased maximum likelihood estimator.