Quaternionic Quantum Dynamics on Complex Hilbert Spaces

TL;DR

This paper demonstrates that quaternionic quantum states, measurements, and channels can be simulated using standard complex quantum information processes, bridging the two formalisms.

Contribution

It introduces methods to simulate quaternionic quantum processes with conventional complex quantum algorithms, expanding the understanding of quaternionic quantum theory.

Findings

Quaternionic quantum measurements can be simulated by complex POVMs.

Quaternionic quantum channels can be simulated by completely positive trace-preserving maps.

All quaternionic quantum processes can be mapped to standard quantum information algorithms.

Abstract

We consider a quaternionic quantum formalism for the description of quantum states and quantum dynamics. We prove that generalized quantum measurements on physical systems in quaternionic quantum theory can be simulated by usual quantum measurements with positive operator valued measures on complex Hilbert spaces. Furthermore, we prove that quaternionic quantum channels can be simulated by completely positive trace preserving maps on complex matrices. These novel results map all quaternionic quantum processes to algorithms in usual quantum information theory.