Quantum Fisher information with coherence

Abstract

In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.

Resolution limits of spatial mode demultiplexing with noisy detection

“…The upper bounds in Eqs. (25) and (27) are essentially the same condition that is present also for the noiseless binary SPADE. It speci¯es the valid range of d before we need to consider the measurements with higher order modes.…”

“…Of course, Eqs. (25) and (27) are only meaningful if the inequalities hold consistently, i.e. SNR ) 1 a priori.…”

“…The consequences and importance of some of these assumptions, and the possibility of relaxing or incorporating them, have been a subject of a number of recent works. [16][17][18][19][20][21][22][23][24][25] In this paper, we address the e®ects of detection noise on the super-resolving power of the SPADE technique. The organization of this paper is as follows.…”

Interferometric sensing of the tilt angle of a Gaussian beam

“…A small tilt of the angle of the object deflects the beam. We note that in some instances this problem can be similar to that of resolving two coherent point sources [29]. However, the role of the field as a controllable probe provides the freedom to consider the initial parameters of the beam, as well as the configuration of the interferometer, toward estimating the tilt angle.…”

“…(c) Interferometric method in which the object is placed inside a Mach-Zehnder interferometer that is also constructed with a PBS. or partially coherent radiation, leading to a debate concerning the attainable precision at the limit of small source separation [26][27][28][29]. In addition, quantum estimation theory provides a context that is suitable for the application of quantum correlations to many optical metrological tasks [19,30,31].…”