Optimal Estimation of Conjugate Shifts in Position and Momentum by Classically Correlated Probes and Measurements

Multiparameter estimation is necessary for force sensing due to simultaneous and nontrivial small changes of position momentum. The design quantum probes that allow all parameters therefore an important task. optimal methods the conjugate momentum harmonic oscillator employ in entangled or non-Gaussian states. We show same results can be obtained a significantly more feasible fashion by employing independent sets differently squeezed Gaussian states classically correlated with measurements. This result demonstrates unexplored power classical correlation between probe measurements directly applicable sensing.