Communication between inertial observers with partially correlated reference frames

TL;DR

This paper investigates quantum communication between inertial observers with partially known Lorentz transformations, analyzing how partial reference frame correlations impact communication efficiency and generalizing previous uncorrelated frame results.

Contribution

It introduces a framework for understanding quantum communication with partially correlated inertial reference frames and analyzes the effects of Lorentz transformations on communication efficiency.

Findings

Partial knowledge of Lorentz transformations affects communication efficiency.

Results recover previous uncorrelated frame studies as special cases.

Analysis covers both pure rotations and boosts.

Abstract

In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analysing the effects on communication when the parties have partial knowledge about the transformation relating their frames, when the transformation is either a rotation or pure boost. This then enables us to investigate how the efficiency of communication is affected due to partially correlated inertial reference frames related by an arbitrary Lorentz transformation. Furthermore, we show how the results of previous studies where reference frames are completely uncorrelated are recovered from our results in appropriate limits.