Ruling out the class of statistical processes involving two noninteracting identical particles in two modes

TL;DR

This paper explores a class of statistical processes involving two noninteracting identical particles in two modes within the GPT framework, identifying which can be realized quantum mechanically and which cannot.

Contribution

It introduces a new physicality condition called the evolution condition that rules out certain processes not realizable in quantum mechanics.

Findings

Certain statistical processes cannot be realized quantum mechanically.

The evolution condition distinguishes quantum-realizable processes.

All processes satisfying three physicality conditions can be implemented with beam splitters.

Abstract

In the framework of Generalized probabilistic theories (GPT), we illustrate a class of statistical processes in case of two noninteracting identical particles in two modes that satisfies a well motivated notion of physicality conditions namely the double stochasticity and the no-interaction condition proposed by Karczewski et. al. (Phys. Rev. Lett. 120, 080401 (2018)), which can not be realized through a quantum mechanical process. This class of statistical process is ruled out by an additional requirement called the evolution condition imposed on two particle evolution. We also show that any statistical process of two noninteracting identical particles in two modes that satisfies all of the three physicality conditions can be realized within quantum mechanics using the beam splitter operation.