Quantum limits to estimation of photon deformation

TL;DR

This paper investigates the fundamental quantum limits of detecting deviations from bosonic behavior in photons, revealing that while detection is theoretically feasible with current technology, the inherent inefficiency poses significant challenges.

Contribution

It introduces a quantum estimation framework for photon deformation, analyzing different classes of deformations and identifying the potential and limitations of current measurement techniques.

Findings

Intensity measurements can detect boson deformation in principle.

Quantum signal-to-noise ratio diminishes with deformation magnitude.

High-energy thermal states may improve detection feasibility.

Abstract

We address potential deviations of radiation field from the bosonic behaviour and employ local quantum estimation theory to evaluate the ultimate bounds to precision in the estimation of these deviations using quantum-limited measurements on optical signals. We consider different classes of boson deformation and found that intensity measurement on coherent or thermal states would be suitable for their detection making, at least in principle, tests of boson deformation feasible with current quantum optical technology. On the other hand, we found that the quantum signal-to-noise ratio (QSNR) is vanishing with the deformation itself for all the considered classes of deformations and probe signals, thus making any estimation procedure of photon deformation inherently inefficient. A partial way out is provided by the polynomial dependence of the QSNR on the average number of photon, which suggests that, in principle, it would be possible to detect deformation by intensity measurements on high-energy thermal states.