2020/06/17 by David Ellerman, Ellerman, David
Physics and Astronomy · #03B48 #46L53 #FOS: Mathematics #FOS: Physical sciences #Probability (math.PR) #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2006.09918
openalex publication_date 2020/06/17 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In finite probability theory, events are subsets of the outcome set. Subsets\ncan be represented by 1-dimensional column vectors. By extending the\nrepresentation of events to two dimensional matrices, we can introduce\n"superposition events." Probabilities are introduced for classical events,\nsuperposition events, and their mixtures by using density matrices. Then\nprobabilities for experiments or `measurements' of all these events can be\ndetermined in a manner exactly like in quantum mechanics (QM) using density\nmatrices. Moreover the transformation of the density matrices induced by the\nexperiments or `measurements' is the Luders mixture operation as in QM. And\nfinally by moving the machinery into the n-dimensional vector space over Z2,\ndifferent basis sets become different outcome sets. That `non-commutative'\nextension of finite probability theory yields the pedagogical model of quantum\nmechanics over Z2 that can model many characteristic non-classical results of\nQM.\n