States and channels in quantum mechanics without complex numbers
Jarosław Adam Miszczak · 2016
In this work we demonstrate a simplified version of quantum mechanics in which the states are constructed using real numbers only. In the standard for-mulation of quantum mechanics the state is represented by positive semidefinite, normalized linear operators. In the following we focus on linearity and hermic-ity properties of density matrices as they are crucial for the properties of quantum channels. The main advantage of the introduced approach is that the simulation of the n-dimensional quantum system requires O(n2) real numbers, in contrast to the standard case where O(n4) real numbers are required. The main disadvantage is the lack of hermicity in the representation of quantum states. This leads to the occurrence of complex eigenvalues of the real-valued density matrices. During the last few years Mathematica computing system has become very popular in the area of quantum information theory and the foundations of quantum mechanics. The main reason for this is its ability to merge the symbolic and nu-