Entanglement or non-separa­bility constitutes a cornerstone of quantum mechanics from which many of its unique charac­teristics arise. For example, non-separa­bility in entangled particle pairs leads to apparent instan­taneous transfer of information and counter­intuitive states of matter. Such phenomena find appli­cations in diverse areas, such as quantum computing or quantum crypto­graphy. Nevertheless, non-separabi­lity is also ubiquitous in the classical domain. Indeed, even prism dispersion of light as observed by Newton over three centuries ago can be considered as an example of non-separable light. However, non-separabi­lity in classical systems, or classical ent­anglement is little explored and in a fragmented fashion, while its potential is certainly not fully exploited.

Over the last few years, there has been a surge of interest in non-separable optical systems, typically involving free-space propa­gating beams and pulses. To this end, the on-demand design and generation of non-separable classical states of light using its various degrees of freedom, such as space, polari­zation, frequency, and propagation path amongst others has become crucial. The concept of non-separa­bility in optics is now being extended to space-time non-separable pulses and ray-wave coupled geometric light. Recently, two researchers from UK and Mexico propose a compre­hensive review of non-separa­bility in classical light providing a perspective on the opportunities for both fundamental science and applications. This review provides a bird’s eye view on the rapidly growing, but incoherent, body of work on non-separable classical states involving different degrees of freedom of light and will introduce a unified framework for their classi­fication, which is extremely timely and of much needed per­spective on the field and its applications. 

First, the researchers illustrate the simi­larities and differences between classical and quantum light states by tutorial examples including coherent states and cat states. This is followed by a mathe­matical description of classical light states borrowing tools from quantum mechanics and showing formal analogies between quantum states and classical eigen­modes. More precisely, it shows that non-separable states of classical light can be derived from a Schrö­dinger-like equation. This in turn allows to describe many properties of classical light with methods typically employed in quantum mechanics, thus providing a theoretical framework to construct classical non-separable states.

Classical non-separable states with two degrees of freedom can be described analogously to bipartite entangled quantum states (e.g. Bell state). Here discuss classical analogs of two-dimen­sional Bell states, such as space-polari­zation non-separable states (e.g. vector vortex beams) and space-time non-separable states as higher-dimen­sional Bell states (e.g. focused pancake pulses); Examples of other bipartite states with it classical analog structured light are also discussed.

The researchers discuss non-separable states with multiple degrees of freedom, e.g. the quantum Green­berger–Horne–Zeilinger state. Such exotic states of structured light include the ray-wave-polari­zation non-separable beam and space-time-polari­zation non-separable pulse. They set up a roadmap for the development of classical non-separable states and give perspective on challenges as well as potential applications in optical metrology, sensing, optical communi­cation, crypto­graphy, computation. So, new oppor­tunities of diversified non-separable states of light are presented for both funda­mental science and appli­cations in the near future. (Source: LPC / CAS)

Reference: Y. Shen & C. Rosales-Guzmán: Nonseparable States of Light: From Quantum to Classical, Laser & Phot. Rev., online 27 April 2022; DOI: 10.1002/lpor.202100533

Links: Optoelectronics Research Centre, University of Southampton, Southampton, UK • Centro de Investigaciones en Óptica, León, México