Geometric model for the electron spin correlation

2021/08/17 by Cetto, Ana María
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2108.07869

Abstract

The quantum formula for the spin correlation of the bipartite singlet spin state, C_Q(\boldsymbola,\boldsymbolb), is derived on the basis of a probability distribution ρ(ϕ) that is generic, i. e., independent of (\boldsymbola,\boldsymbolb). In line with a previous result obtained within the framework of the quantum formalism, the probability space is partitioned according to the sign of the product A=αβ of the individual spin projections α and β onto \boldsymbola and \boldsymbolb. A specific partitioning and a corresponding set of realizations ϕ are associated with every measurement setting (\boldsymbola,\boldsymbolb); this precludes the transfer of α or β from C_Q(\boldsymbola,\boldsymbolb) to C_Q(\boldsymbola,\boldsymbolb'), for \boldsymbolb'≠\boldsymbolb. A geometric model that reproduces the spin correlation serves to validate our approach, giving a concrete meaning to the quantum result in terms of a (local random variable) probability distribution.

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