Quaternionic Quantum Dynamics on Complex Hilbert Spaces

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.

5 pages

References in corpus (5)

• Limited Holism and Real-Vector-Space Quantum Theory
• Simulating quantum systems using real Hilbert spaces
• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
• Entanglement Sharing in Real-Vector-Space Quantum Theory
• Quaternionic Computing

Cited by in corpus (8)

• The SIC Question: History and State of Play
• An introduction to operational quantum dynamics
• Virial theorem and generalized momentum in quaternic quantum mechanics
• Self-interacting quantum particles
• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Self-interacting quantum particles and the Dirac delta potential
• Quantum self-interaction within an infinitely deep cavity
• Gleason's Theorem for a Qubit as Part of a Composite System