Ultimate precision bound of quantum and sub-wavelength imaging

TL;DR

This paper establishes the fundamental quantum limits on the resolution of far-field imaging, showing that quantum correlations can enable super-resolution beyond classical limits.

Contribution

It introduces a quantum framework for determining the ultimate resolution bounds in imaging, including a simple formula for thermal sources and the role of quantum correlations.

Findings

Resolution scales with photon number according to the standard quantum limit.

Quantum-correlated sources can achieve super-resolution below the Rayleigh limit.

The bounds apply universally to any quantum-based imaging technology.

Abstract

We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation between two point-like sources is equivalent to the estimation of the loss parameters of two lossy bosonic channels, i.e., the transmissivities of two beam splitters. Using this representation, we establish the ultimate precision bound for resolving two point-like sources in an arbitrary quantum state, with a simple formula for the specific case of two thermal sources. We find that the precision bound scales with the number of collected photons according to the standard quantum limit. Then we determine the sources whose separation can be estimated optimally, finding that quantum-correlated sources (entangled or discordant) can be super-resolved at the sub-Rayleigh scale. Our results set the upper bounds on any present or future imaging technology, from astronomical observation to microscopy, which is based on quantum detection as well as source engineering.