# Relativistically invariant photonic wave packets

## TL;DR

This paper introduces a relativistically invariant photonic wave packet construction that maintains its quantum state across reference frames, enabling robust free-space communication using helicity encoding and simple measurement techniques.

## Contribution

It presents a novel wave packet design that is immune to Lorentz transformations and guarantees perfect distinguishability with straightforward helicity measurements.

## Key findings

- Wave packets remain invariant under Lorentz transformations.
- Helicity encoding is effective for free-space quantum communication.
- Simple helicity measurements ensure perfect state distinguishability.

## Abstract

We present a photonic wave packet construction which is immune against the decoherence effects induced by the action of the Lorentz group. The amplitudes of a pure quantum state representing the wave packet remain invariant irrespective of the reference frame into which the wave packet has been transformed. Transmitted information is encoded in the helicity degrees of freedom of two correlated momentum modes. The helicity encoding is considered to be particularly suitable for free-space communication. The integral part of the story is information retrieval on the receiver's side. We employed probably the simplest possible helicity (polarization) projection measurement originally studied by Peres and Terno. Remarkably, the same conditions ensuring the invariance of the wave packet also guarantee perfect distinguishability in the process of measuring the helicity.