Abstract
Multiparameter quantum estimation is made difficult by the following three obstacles. First, incompatibility among different physical quantities poses a limit on the attainable precision. Second, the ultimate precision is not saturated until you discover the optimal measurement. Third, the optimal measurement may generally depend on the target values of parameters, and thus may be impossible to perform for unknown target states. We present a method to circumvent these three obstacles. A class of quantum statistical models, which utilizes antiunitary symmetries or, equivalently, real density matrices, offers compatible multiparameter estimations. The symmetries accompany the target-independent optimal measurements for pure-state models. Based on this finding, we propose methods to implement antiunitary symmetries for quantum metrology schemes. We further introduce a function which measures antiunitary asymmetry of quantum statistical models as a potential tool to characterize quantumness of phase transitions.
Highlights
The measurement incompatibility is troubling for quantum metrological tasks which aim at estimating parameters with ever in
Whether or not the quantum CramérRao bounds (QCRBs) is saturated, identifying attainable precision limit is the first step of quantum multiparameter metrology
Any quantum statistical model endowed with an antiunitary symmetry is compatible, which means that the QCRB is attainable in the asymptotic limit
Summary
Incompatibility residing in simultaneous measurements of different quantities has been a widely acknowledged character of quantum mechanics. Whether or not the QCRB is saturated, identifying attainable precision limit is the first step of quantum multiparameter metrology. This article proposes the use of antiunitary symmetries to side-step the problems of incompatibility and unfeasible measurement in multiparameter quantum estimation. Any quantum statistical model endowed with an antiunitary symmetry is compatible, which means that the QCRB is attainable in the asymptotic limit. Our optimal measurement has a continuous degree of freedom, and one can choose any of them to achieve the global optimality With these advantages in mind, we present methods to implement antiunitary symmetries in multiparameter quantum metrology.
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