# Transformation properties and entanglement of relativistic qubits under space-time and gauge transformations

## TL;DR

This paper clarifies how relativistic qubits transform under space-time and gauge changes, providing a simplified, generalized framework that enhances understanding of entanglement behavior in relativistic quantum systems.

## Contribution

It introduces a Lorentz invariant formulation of relativistic qubits that clarifies previous misconceptions and simplifies the analysis of their transformation properties and entanglement.

## Key findings

- Clarified the transformation properties of qubits under Lorentz and gauge transformations.
- Provided a simplified, more intuitive framework for analyzing relativistic qubits.
- Generalized previous results on entanglement behavior in relativistic settings.

## Abstract

We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic quantum information theory. We then use this formulation to consider the transformation properties of qubits and density matrices under space-time and gauge transformations. Finally we use our results to understand the behaviour of entanglement between different partitions of quantum systems. Our approach not only clarifies the notation, but provides a more intuitive and simple way of gaining insight into the behaviour of relativistic qubits. In particular, it allows us to greatly generalize the results in the current literature as well as substantially simplifying the calculations that are needed.