Three measures of fidelity for photon states

TL;DR

This paper explores an alternative approach to photon state description using relativistic quantum mechanics, revealing new fidelity measures that help characterize photon localization, differing from traditional field quantization methods.

Contribution

It introduces new fidelity measures for photon states derived from relativistic quantum mechanics, providing a different perspective from standard electromagnetic field quantization.

Findings

New fidelity measures for photon states are proposed.

Relativistic quantum mechanics offers a different framework for photon description.

Photon localization can be characterized using these new fidelity measures.

Abstract

We show that the standard method of introducing the quantum description of the electromagnetic field -- by canonical field quantization -- is not the only one. We have chosen here the relativistic quantum mechanics of the photon as the starting point. The treatment of photons as elementary particles merges smoothly with the description in terms of the quantized electromagnetic field but it also reveals some essential differences. The most striking result is the appearance of various measures of fidelity for quantum states of photons. These measures are used to characterize the localization of photons.