Entanglement in Classical Optics

TL;DR

This paper reviews the concept of entanglement in classical optics, comparing it with quantum entanglement, and explores its potential for simulating quantum information processing due to its robustness.

Contribution

It introduces new theorems to distinguish separable and nonseparable states in classical wave optics and discusses classical analogs of quantum Bell-like states.

Findings

Classical entanglement can produce Bell-like states.

New theorems discriminate between separable and nonseparable states.

Classical polarization optics can simulate certain quantum information tasks.

Abstract

The emerging field of entanglement or nonseparability in classical optics is reviewed, and its similarities with and differences from quantum entanglement clearly pointed out through a recapitulation of Hilbert spaces in general, the special restrictions on Hilbert spaces imposed in quantum mechanics and the role of Hilbert spaces in classical polarization optics. The production of Bell-like states in classical polarization optics is discussed, and new theorems are proved to discriminate between separable and nonseparable states in classical wave optics where no discreteness is involved. The influence of the Pancharatnam phase on a classical Bell-like state is deived. Finally, to what extent classical polarization optics can be used to simulate quantum information processing tasks is also discussed. This should be of great practical importance because coherence and entanglement are robust in classical optics but not in quantum systems.