# Universal Transformation of Displacement Operators and its Application to Homodyne Tomography In Differing Relativistic Reference Frames

## TL;DR

This paper develops a universal method to transform displacement operators between relativistic reference frames, revealing distortions in phase and amplitude that impact homodyne detection, and proposes a robust detection scheme for relativistic quantum systems.

## Contribution

It introduces a generic transformation method for displacement operators across relativistic frames and proposes an ideal homodyne detection scheme resilient to relativistic distortions.

## Key findings

- Traditional homodyne detection can fail in non-inertial frames.
- The proposed ideal homodyne scheme maintains quantum information extraction.
- Relativistic effects distort phase and modal structures in quantum systems.

## Abstract

In this paper, we study how a displacement of a quantum system appears under a change of relativistic reference frame. We introduce a generic method in which a displacement operator in one reference frame can be transformed into another reference frame. It is found that, when moving between non-inertial reference frames there can be distortions of phase information, modal structure and amplitude. We analyse how these effects affect traditional homodyne detection techniques. We then develop an in principle homodyne detection scheme which is robust to these effect, called the ideal homodyne detection scheme. We then numerically compare traditional homodyne detection with this in principle method and illustrate regimes when the traditional homodyne detection schemes fail to extract full quantum information.