Informational Approach to Identical Particles in Quantum Theory

TL;DR

This paper derives the symmetrization postulate in quantum theory from an informational perspective, showing that indistinguishable particles must be symmetrized or antisymmetrized, excluding other variants like anyonic behavior.

Contribution

It introduces an operational indistinguishability postulate that derives the symmetrization postulate purely from informational principles, clarifying its fundamental nature.

Findings

The symmetrization postulate can be derived from informational constraints.

No natural variants of the symmetrization postulate exist.

Anyonic behavior is excluded by the derivation.

Abstract

A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via the symmetrization postulate, which restricts a system of identical particles to the set of symmetric states (`bosons') or the set of antisymmetric states (`fermions'). However, the physical basis and range of validity of the symmetrization postulate has not been established. A well-known topological derivation of the postulate implies that its validity depends on the dimensionality of the space in which the particles move. However, this derivation relies on the labeling of indistinguishable particles, a notion that cannot be justified on an informational basis. Here we show that the symmetrization postulate can be derived by strictly adhering to the informational requirement that particles which cannot be experimentally distinguished from one another are not labeled. Our key novel postulate is the operational indistinguishability postulate, which posits that the amplitude of a process involving several indistinguishable particles is determined by the amplitudes of all possible transitions of these particles when treated as distinguishable. The symmetrization postulate follows by requiring consistency with the rest of the quantum formalism. The derivation implies that the symmetrization postulate admits no natural variants. In particular, the possibility that identical particles generically exhibit anyonic behavior in two dimensions is excluded.