A semidefinite program over quadratic phase-space observables computes the Holevo Cramér-Rao bound for Gaussian states with parameters encoded in both the first moments and the covariance matrix.
Quantum multiphase estimation
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abstract
Quantum phase estimation is fundamental to advancing quantum science and technology. While much of the research has concentrated on estimating a single phase, the simultaneous estimation of multiple phases can yield significantly enhanced sensitivities when using specially tailored input quantum states. This work reviews recent theoretical and experimental advancements in the parallel estimation of multiple arbitrary phases. We highlight strategies for constructing optimal measurement protocols and discuss the experimental platforms best suited for implementing these techniques.
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Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cram\'er-Rao bounds
A semidefinite program over quadratic phase-space observables computes the Holevo Cramér-Rao bound for Gaussian states with parameters encoded in both the first moments and the covariance matrix.