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

Multiparameter quantum metrology in the Heisenberg Limit regime: many repetition scenario vs. full optimization

“…The nontrivial question is, if the sum of variances for the optimal joint measurement will follow a similar scaling-it may turn out that the existence of the advantage depends on paradigm chosen. As recently shown in [61], for the multiphases estimation problem in a multiarm interferometer, this issue does not lead to divergent conclusions-even if the scaling of the total cost with the number of the parameters depends on the paradigm, the potential advantage obtainable by measuring all of the parameters jointly instead of separately is very similar in both paradigms. In this paper we analyze this issue more generally and show that result is not universal-it may happen that existence or absence of the advantage indeed depends on the paradigm chosen.…”

“…C for more details and discussion about applicability of this approach to a many parameter problem. See also [32,61,71] for further discussion about optimization of region discrimination in the first part of the above construction, as well as a general discussion about this bound for finite N .…”

“…2. As shown in [61], if all the generators mutually commute ∀ i [Λ i , Λ j ] = 0, there is no asymptotic advantage (for large N ) in using a general adaptive strategy when compered to the parallel one. Therefore when analyzing the first two examples, we will focus on the parallel scheme only.…”

“…Many repetition scenario has been considered in [45][46][47][48][49](using multiparameter quantum CR Rao bound) and [26,[50][51][52]) (using tighter variants of quantum CR bound), while single experiment scenarios where the total amount of resources is limited has been analyzed mainly within the Bayesian paradigm for models with underlying group symmetry (covariant problems)-SU(2)/U(1) [53,54], SU (2) [55][56][57][58], SO(3) [59], SU(d) [60]. The quantitative analysis of the relation between the results obtained within these two paradigms has started to be analyzed only very recently [61].…”

“…The most pressing question is whether a gain can be made by measuring all the parameters simultaneously instead of separately, while consuming the same total amount of resources? That the necessity of splitting these resources between experiments focusing on estimating a given parameter in the separate case, will in general have different consequences in different paradigms [61]. If only the total amount of resources N is restricted, and p parameters are to be esti- Optimal achievable sum of variances of estimated parameters for six different models with unitary evolution governed by the Hamiltonian θiΛi.…”