Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously

We characterize operationally meaningful quantum gains in a paradigmatic model of lossless multiple-phase interferometry and stress the insufficiency of the analysis based solely on the concept of quantum Fisher information. We show that the advantage of the optimal simultaneous estimation scheme amounts to a constant factor improvement when compared with schemes where each phase is estimated separately, which is contrary to widely cited results claiming a better precision scaling in terms of the number of phases involved.

Figure 1

Multiple-phase estimation schemes where a constraint is imposed on the total resources used (left column) or resources used in a single experiment (right column). The top and bottom rows represent, respectively, the protocols where all the phases are measured jointly or the estimation procedure is repeated for each of the phases separately. The lower bounds for the sum of variances obtainable within each of (i)–(iv) paradigms is presented in Table 1.