Imaginarity-free quantum multiparameter estimation

TL;DR

This paper introduces a method leveraging antiunitary symmetries to enable compatible, target-independent quantum multiparameter estimation, overcoming key obstacles like incompatibility and measurement dependence.

Contribution

It proposes utilizing antiunitary symmetries in quantum models to achieve compatible and optimal multiparameter estimation independent of target states.

Findings

Compatible multiparameter estimation via antiunitary symmetries

Target-independent optimal measurements for pure states

Antiunitary asymmetry as a tool for phase transition characterization

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.