Entanglement and Complete Positivity: Relevance and Manifestations in Classical Scalar Wave Optics

TL;DR

This paper explores how concepts like entanglement and complete positivity, typically associated with quantum mechanics, are relevant and manifest in classical scalar wave optics, especially in Gaussian beam propagation and properties.

Contribution

It demonstrates the relevance of quantum information concepts in classical optics, analyzing Gaussian beams and Twisted Gaussian Schell Model beams through these frameworks.

Findings

Propagation characteristics reveal entanglement signatures in beam width evolution.

Partial transpose explains key properties of TGSM beams.

Classical optics can exhibit phenomena analogous to quantum entanglement.

Abstract

Entanglement of states and Complete Positivity of maps are concepts that have achieved physical importance with the recent growth of quantum information science. They are however mathematically relevant whenever tensor products of complex linear (Hilbert) spaces are involved. We present such situations in classical scalar paraxial wave optics where these concepts play a role: propagation characteristics of coherent and partially coherent Gaussian beams; and the definition and separability of the family of Twisted Gaussian Schell Model (TGSM) beams. In the former, the evolution of the width of a projected one-dimensional beam is shown to be a signature of entanglement in a two-dimensional amplitude. In the latter, the partial transpose operation is seen to explain key properties of TGSM beams.