Joint estimation of phase and phase diffusion for quantum metrology

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M. D. Vidrighin, G. Donati, M. G. Genoni, X.-M. Jin, W. S. Kolthammer, M. S. Kim, A. Datta, M. Barbieri, I. A. Walmsley
Nature Communications 5, 3532 (2014)

Phase estimation is one of the most studied quantum metrology situations, with wide-ranging practical applications. In many realistic situations, phase and phase diffusion may vary in time. Consequently, the accuracy of phase estimation may be affected by varying estimates of the magnitude of phase diffusion.

In their work, Vidrighin and co-workers investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states. For these cases, a trade-off bound is derived on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. This bound is then used to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry.