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States and channels in quantum mechanics without complex numbers. (English) Zbl 1386.81018
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 305-316 (2017).
Summary: In the presented work, 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.
For the entire collection see [Zbl 1379.13001].
MSC:
81P15 Quantum measurement theory, state operations, state preparations
94A40 Channel models (including quantum) in information and communication theory
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
81P16 Quantum state spaces, operational and probabilistic concepts
81P40 Quantum coherence, entanglement, quantum correlations
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