Quaternionic Quantum Dynamics on Complex Hilbert Spaces

Foundations of Physics 43 (5):656-664 (2013)

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
Keywords Quantum foundations  Quaternions  Division rings  Born rule  Quaternionic POVMs  Quaternionic quantum channels
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DOI 10.1007/s10701-013-9708-6
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