Selective correlations in finite quantum systems and the Desargues property

TL;DR

This paper explores a geometric property called Desargues in classical and quantum systems, revealing how it leads to selective correlations in logical circuits and quantum measurement experiments, highlighting a novel link between geometry and physics.

Contribution

It introduces a quantum analogue of the Desargues property, demonstrating its implications for correlations in classical logic circuits and quantum measurement processes.

Findings

Classical circuits exhibit selective correlations based on the Desargues property.

Quantum experiments show correlated outcomes when certain projective measurements are aligned.

The Desargues property provides a geometric framework for understanding correlations in physics.

Abstract

The Desargues property is well known in the context of projective geometry. An analogous property is presented in the context of both classical and Quantum Physics. In a classical context, the Desargues property implies that two logical circuits with the same input, show in their outputs selective correlations. In general their outputs are uncorrelated, but if the output of one has a particular value, then the output of the other has another particular value. In a quantum context, the Desargues property implies that two experiments each of which involves two successive projective measurements, have selective correlations. For a particular set of projectors, if in one experiment the second measurement does not change the output of the first measurement, then the same is true in the other experiment.