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Multiphase estimation is a paradigmatic example of a multiparameter problem.When measuring multiple phases embedded in interferometric networks,specially-tailored input quantum states achieve enhanced sensitivities comparedwith both single-parameter and classical estimation schemes. Significantattention has been devoted to defining the optimal strategies for the scenarioin which all of the phases are evaluated with respect to a common referencemode, in terms of optimal probe states and optimal measurement operators. Aswell, the strategies assume unlimited external resources, which isexperimentally unrealistic. Here, we optimize a generalized scenario thattreats all of the phases on an equal footing and takes into account theresources provided by external references. We show that the absence of anexternal reference mode reduces the number of simultaneously estimatableparameters, owing to the immeasurability of global phases, and that thesymmetries of the parameters being estimated dictate the symmetries of theoptimal probe states. Finally, we provide insight for constructing optimalmeasurements in this generalized scenario. The experimental viability of thiswork underlies its immediate practical importance beyond fundamental physics.

Multiphase estimation without a reference mode