Quantum limits of superresolution in a noisy environment

TL;DR

This paper investigates the fundamental quantum limits of resolving two identical sources in noisy environments, demonstrating that noise causes the resolution to deteriorate to zero as sources become indistinguishable.

Contribution

It proves that noise-induced false excitations cause the quantum Fisher information to vanish at small separations, establishing a fundamental limit to superresolution under realistic noisy conditions.

Findings

Quantum Fisher information approaches zero with noise, limiting resolution.

False excitations like thermal noise and dark counts impair superresolution.

Finite spatial mode analysis quantifies noise impact on resolving thermal sources.

Abstract

We analyze the ultimate quantum limit of resolving two identical sources in a noisy environment. We prove that in the presence of noise causing false excitation, such as thermal noise, the quantum Fisher information of arbitrary quantum states for the separation of the objects, which quantifies the resolution, always converges to zero as the separation goes to zero. Noisy cases contrast with a noiseless case where it has been shown to be nonzero for a small distance in various circumstances, revealing the superresolution. In addition, we show that false excitation on an arbitrary measurement, such as dark counts, also makes the classical Fisher information of the measurement approach to zero as the separation goes to zero. Finally, a practically relevant situation resolving two identical thermal sources, is quantitatively investigated by using the quantum and classical Fisher information of finite spatial mode multiplexing, showing that the amount of noise poses a limit on the resolution in a noisy system.