States and channels in quantum mechanics without complex numbers

In the presented note we aim at exploring the possibility of abandoning complex numbers in the representation of quantum states and operations. We demonstrate a simplified version of quantum mechanics in which the states are represented using real numbers only. The main advantage of this approach is...

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Bibliographic Details
Published in:arXiv.org 2016-03
Main Author: Miszczak, J A
Format: Article
Language:English
Subjects:
Channels
Complex numbers
Computer algebra
Computer simulation
Quantum mechanics
Quantum physics
Quantum theory
Real numbers
Representations
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Summary:In the presented note we aim at exploring the possibility of abandoning complex numbers in the representation of quantum states and operations. We demonstrate a simplified version of quantum mechanics in which the states are represented using real numbers only. The main advantage of this approach is that the simulation of the \(n\)-dimensional quantum system requires \(n^2\) real numbers, in contrast to the standard case where \(n^4\) real numbers are required. The main disadvantage is the lack of hermicity in the representation of quantum states. Using Mathematica computer algebra system we develop a set of functions for manipulating real-only quantum states. With the help of this tool we study the properties of the introduced representation and the induced representation of quantum channels.
ISSN:2331-8422
DOI:10.48550/arxiv.1603.04787