A Pseudo-Unitary Version of Schwinger's Symbolism of Atomic Measurements and a Prospect for a New Relativistic Quantum Information Theory

TL;DR

This paper extends quantum measurement theory into a relativistic covariant framework using Cartan's space and the conformal group, aiming to develop a relativistic quantum information theory that preserves non-relativistic measurement principles.

Contribution

It introduces a pseudo-unitary covariant formulation of quantum measurements within special relativity, linking non-relativistic quantum mechanics to a relativistic context using SU(2,2).

Findings

Correlations between spacetime-separated measurements are consistent with relativistic covariance.

Supports the idea that quantum inner structure can be described within special relativity.

Provides a foundation for covariant quantum computational gates and entanglement formation.

Abstract

The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincar\'e subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schr\"odinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.