# Quantum-mechanical description of entanglement between photon's polarization and momentum

## TL;DR

This paper develops a quantum framework describing how a photon's polarization and momentum become entangled, revealing that gauge degrees of freedom influence observable entanglement effects.

## Contribution

It introduces a quantum description linking polarization and momentum entanglement via Jones vectors and gauge degrees of freedom, advancing understanding of photon entanglement.

## Key findings

- Polarization entanglement depends on gauge choices.
- Jones vector functions as a polarization wavefunction.
- Gauge degrees of freedom have observable effects.

## Abstract

It has been accepted that the polarization of the photon in vector beams is entangled with its momentum. Here a quantum description is advanced for the polarization that shows entanglement with the momentum. This is done by showing that the Jones vector at each value of the momentum plays the role of the polarization wavefunction in the sense that the Pauli matrices represent the Cartesian components of the polarization in the local reference system with respect to which the Jones vector is defined. The unit vector that the constraint of transversality condition requires to specify the local reference system turns out to be a gauge degree of freedom that determines the entanglement of the polarization with the momentum and has observable effects.