Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability

TL;DR

This paper extends Hardy-type logical gadgets to classical graph-theoretic structures, enabling the analysis of correlations and properties of quantum observables, with implications for quantum-classical comparisons.

Contribution

It introduces a method to generalize Hardy-type gadgets to classical graph structures for analyzing quantum observable correlations.

Findings

Generalization of Hardy-type gadgets to classical graphs

New methods for representing quantum observables faithfully

Extensions to relational properties predicting observable equality

Abstract

In quantum logical terms, Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. If interpreted classically those structures serve as graph-theoretic "gadgets" that enforce correlations on the respective preselected and postselected observable terminal points. The method allows the generalization and extension to other types of relational properties, in particular, to novel joint properties predicting classical equality of quantum mechanically distinct observables. It also facilitates finding faithful orthogonal representations of quantum observables.