States and channels in quantum mechanics without complex numbers

Abstract

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.

10 pages, 2 figures, presented at ACA2015, July 20-23, 2015, Kalamata, Greece

References in corpus (4)

• Singular value decomposition and matrix reorderings in quantum information theory
• Generating and using truly random quantum states in Mathematica
• QCWAVE, a Mathematica quantum computer simulation update
• Employing online quantum random number generators for generating truly random quantum states in Mathematica