Penrose dodecahedron, Witting configuration and quantum entanglement

TL;DR

This paper explores entangled spin-3/2 particles modeled by dodecahedral geometry and Witting configurations, analyzing their symmetries and quantum circuit representations to understand non-locality and entanglement.

Contribution

It introduces a detailed analysis of entangled systems based on Witting configurations, highlighting symmetry increases and quantum circuit modeling for such geometric quantum states.

Findings

Duplication of points increases symmetry by a factor of 432.

Witting configurations provide a geometric framework for entanglement.

Quantum circuits effectively describe operations on these entangled states.

Abstract

A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose for formulation of analogue of Bell theorem "without probabilities." The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. However, such reformulation needs for some subtleties related with entanglement of two such configurations essential for consideration of non-locality and some other questions. Two entangled systems with quantum states described by Witting configurations are discussed in presented work. Duplication of points with respect to vertices of dodecahedron produces rather significant increase with number of symmetries in 25920/60=432 times. Quantum circuits model is a natural language for description of operations with different states and measurements of such systems.