Three Slit Experiments and the Structure of Quantum Theory

TL;DR

This paper explores the structure of quantum theory through three-slit experiments, analyzing a measure of interference that is zero in quantum mechanics, and characterizes theories where this measure vanishes.

Contribution

It adapts Sorkin's interference measure into a general framework and characterizes theories with zero interference in terms of state determination via two-slit experiments.

Findings

Quantum theory predicts zero interference measure in three-slit experiments.

The class of theories with zero interference allows full state determination from two-slit data.

The framework links interference properties to the structural features of probabilistic theories.

Abstract

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin's measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of 'two-slit' experiments.