Entanglement from longitudinal and scalar photons

TL;DR

This paper demonstrates that longitudinal and scalar photons, arising from covariant quantization in the Lorentz gauge, can generate entanglement between distant atoms or oscillators, with observable effects consistent across gauges.

Contribution

It reveals how different photon types in covariant quantization produce distinct entangled states and shows gauge invariance of physical effects.

Findings

Longitudinal and scalar photons can produce entanglement.

Entangled states differ between Lorentz and Coulomb gauges.

Physical observables remain gauge-invariant.

Abstract

The covariant quantization of the electromagnetic field in the Lorentz gauge gives rise to longitudinal and scalar photons in addition to the usual transverse photons. It is shown here that the exchange of longitudinal and scalar photons can produce entanglement between two distant atoms or harmonic oscillators. The form of the entangled states produced in this way is very different from that obtained in the Coulomb gauge, where the longitudinal and scalar photons do not exist. A generalized gauge transformation is used to show that all physically observable effects are the same in the two gauges, despite the differences in the form of the entangled states. An approach of this kind may be useful for a covariant description of the dynamics of quantum information processing.