Optimal quantum metrology of distant black bodies

Abstract

Measurements of an object's temperature are important in many disciplines, from astronomy to engineering, as are estimates of an object's spatial configuration. We present the quantum optimal estimator for the temperature of a distant body based on the black body radiation received in the far-field. We also show how to perform separable quantum optimal estimates of the spatial configuration of a distant object, i.e. imaging. In doing so we necessarily deal with multi-parameter quantum estimation of incompatible observables, a problem that is poorly understood. We compare our optimal observables to the two mode analogue of lensed imaging and find that the latter is far from optimal, even when compared to measurements which are separable. To prove the optimality of the estimators we show that they minimise the cost function weighted by the quantum Fisher informationthis is equivalent to maximising the average fidelity between the actual state and the estimated one.

Optimal Imaging of Remote Bodies Using Quantum Detectors

“…1. While the parameters of interest |γ| and φ have non-commuting measurement observables, they turn out to be jointly measurable [26].…”

Optimal Imaging of Remote Bodies Using Quantum Detectors

“…Pearce et al showed that the CDC, γðr 1 ; r 2 Þ ¼ jγje iϕ , between two points r 1 and r 2 in the imaging plane can be measured nearly optimally using the setup in Fig. 1 [26]: the two main features are the application of a varying phase, ϕ a , to one mode of incoming light and the measurement using photon-number-resolving detectors. Given the latter, we label this the "Count" scheme.…”

Frontiers of quantum optics: photonics tolls, computational complexity, quantum metrology, and quantum correlations

“…The van Cittert-Zernike theorem relates the CDC to the source distribution via a two-dimensional Fourier transform [204]. Pearce et al [205] showed that the CDC, g(r 1 , r 2 )=|g|e if , between two points r 1 and r 2 in the imaging plane can be measured nearly optimally using the setup in Fig. 4.2.…”

“…The optimality of the Count scheme is claimed under the theoretical model developed in Reference [205] using the quantum Cramér-Rao bound and the quantum Fisher information. The quantum Fisher information F(x ), say for estimating a parameter x , tell us the maximum information one could extract with an optimal measurement.…”

“…In our experiment, the quantum Cramér-Rao bound relates the mean squared error (MSE) matrix for these parameters to the quantum Fisher information matrix determined by the light field captured in the detectors [205,206]. The quantum Fisher information depends on the state of light and the Positive-Operator Valued Measure (POVM) of detection.…”