Particle-wave duality: a dichotomy between symmetry and asymmetry

TL;DR

This paper explores the fundamental link between symmetry and asymmetry in quantum systems, proposing a duality between wave and particle natures, and introduces information-theoretic bounds related to these properties.

Contribution

It establishes a quantitative framework connecting symmetry and asymmetry to wave-particle duality, including bounds on information and implications for entangled systems.

Findings

Maximum information about symmetry and asymmetry is bounded by log of Hilbert space dimension.

Entangled systems can exhibit collective wave-like symmetry while maintaining particle-like asymmetry.

Superdense coding is interpreted as an interference phenomenon related to wave-like symmetry.

Abstract

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.