Quantum metrology: Resolving coherent and partially coherent point sources

Quantum metrology allows increasing the sensitivity of the measurements of the physical parameters by exploiting quantum features of the probes and measurements. The advantages of quantum techniques were already demonstrated experimentally for the problems of phase estimation (that was used for gravitational wave detection) and quantum imaging. An important model example of a quantum imaging problem is the separation estimation of the two point-sources. It allows to better understand the connection between the state of the emitted light, properties of the measurement, and the resulting resolution. In addition, this problem itself has a number of practical applications in astronomical observation, fluorescent microscopy, etc.

Intense analysis of the separation estimation problem during past years showed, that the traditional approach of measuring emitted field intensity (called direct imaging) often leads to the vanishing of the information about the separation when the separation is small. This feature is known as the “Raleigh curse”. At the same time, measurements in specific spatial modes, e.g. Hermit-Gauss modes, do not lead to this kind of problem. Another important aspect of this problem is the state of the emitted light. The role of the sources’ coherence sparked hot debates during recent years, which made us to address this problem. In our research we analyze separation estimation between pair of mutually coherent sources, making no assumptions about quantum statistics of emitted light, absolute and mutual brightness of the sources. We show that anti-bunching of the sources' radiation leads to an increase of the sensitivity, but at the same time ignorance of sources brightness wipes out any possible profit from non-classical statistics of the sources.