Abstract
When two or more degrees of freedom become coupled in a physical system, a number of observables of the latter cannot be represented by mathematical expressions separable with respect to the different degrees of freedom. In recent years it appeared clear that these expressions may display the same mathematical structures exhibited by multiparty entangled states in quantum mechanics. In this work, we investigate the occurrence of such structures in optical beams, a phenomenon that is often referred to as ‘classical entanglement’. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results clarify and shed new light upon the physics underlying this intriguing aspect of classical optics.
Highlights
A composite physical system, namely one made of at least two identifiable parts, say A and B, which are denoted subsystems, can be prepared in such a way that the latter are not independent
In the realm of classical physics this means, for example, that the probability P (a ∈ A, b ∈ B) for the events a, b associated to subsystems A, B, respectively, cannot be factored as P (a ∈ A, b ∈ B) = P (a ∈ A)P (b ∈ B) [1]
For a composite quantum system, statistical dependence of the subsystems A, B means that the state vector ∣Ψ 〉 describing a physical state of the whole system, cannot be decomposed in the tensor product
Summary
A composite physical system, namely one made of at least two identifiable parts, say A and B, which are denoted subsystems, can be prepared in such a way that the latter are not independent. Single-photon-vacuum entanglement resembles classical entanglement in that there is only one individual physical system, a single-photon in the quantum case and a single bright beam in the classical one, and two (or more) entangled modes of the electromagnetic field [17,18,19].
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