Phase estimation with nonunitary interferometers: Information as a metric

Abstract

Determining the phase in one arm of a quantum interferometer is discussed taking into account the three nonideal aspects in real experiments: nondeterministic state preparation, nonunitary state evolution due to losses during state propagation, and imperfect state detection. A general expression is written for the probability of a measurement outcome taking into account these three nonideal aspects. As an example of applying the formalism, the classical Fisher information and fidelity (Shannon mutual information between phase and measurements) are computed for few-photon Fock and N00N states input into a lossy Mach-Zehnder interferometer. These three nonideal aspects lead to qualitative differences in phase estimation, such as a decrease in fidelity and Fisher information that depends on the true value of the phase.

Evaluation of counterfactuality in counterfactual communication protocols

“…However, if the value of θ is fixed but unknown, one might ask oneself how much information, on average, a single use of a specific interferometer yields about θ. This quantity of information is given by the classical Fisher information [13,35]:…”

“…[5] Studies with optical quantum interferometers have shown great promise, not only for the detection of novel physics, but also for external field detection and external parameter estimation. [6][7][8][9][10][11][12][13][14][15][16] A common example of this is phase estimation. By letting optical quantum states interfere with a medium inside an interferometer it can be easier to establish the nature of a phase-shift caused by the medium, than with a direct interaction.…”

“…By letting optical quantum states interfere with a medium inside an interferometer it can be easier to establish the nature of a phase-shift caused by the medium, than with a direct interaction. [10,[17][18][19] A framework for studying phase estimation in interferometers has been developed by Bahder et al [13,18,19]. This framework uses the Shannon mutual information and the classical Fisher information as measures of the phase estimating capacity of different interferometers and input states.…”

Optical interferometry in the presence of large phase diffusion

“…However, in realistic conditions, one has to retrieve phase information that has been unavoidably degraded by different sources of noise, which have to be taken into account in order to evaluate the interferometric precision [24]. The effects of imperfect photodetection in the measurement stage, or the presence of amplitude noise in the interferometric arms have been extensively studied [25][26][27][28][29][30][31][32][33][34][35]. Only recently, the role of phase-diffusive noise in interferometry have been theoretically investigated for optical polarization qubit [36][37][38], condensate systems [39,40], Bose-Josephson junctions [41], and Gaussian states of light [42].…”

Tried-and-true binary strategy for angular displacement estimation based upon fidelity appraisal

“…Therefore, we try to appraise the two strategies by replacing standard deviation with fidelity estimation. In this paper, we report using fidelity [25][26][27] (the Shannon mutual information between the angular displacement θ and the measuring outcomes) to appraise two binary detection strategies whose sensibilities are on a par with each other under the standard deviation metric. A simple understanding for the mutual information is the amount of sender's original information which can be obtained by receiver from the acquired distortion information.…”