A Unified Theory of Classical and Quantum Light

Richard M. Sillitto

Matthew Leifer, Robert W. Spekkens

Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Classical probability theory is independent of causal structure, whereas the conventional quantum formalism requires causal structure to be fixed in advance. In this paper, we develop the formalism of quantum conditional states, which unifies the description of experiments involving two systems at a single time with the description of those involving a single system at two times. The analogies between quantum theory and classical probability theory are expressed succinctly within the formalism and it unifies the mathematical description of distinct concepts, such as ensemble preparation procedures, measurements, and quantum dynamics. We introduce a quantum generalization of Bayes' theorem and the associated notion of Bayesian conditioning. Conditioning a quantum state on a classical variable is the correct rule for updating quantum states in light of classical data, regardless of the causal relationship between the classical variable and the quantum degrees of freedom, but it does not include the projection postulate as a special case. We show that previous arguments that projection is the quantum generalization of conditioning are based on misleading analogies. Since our formalism is causally neutral, conditioning provides a unification of the predictive and retrodictive formalisms for prepare-and-measure experiments and leads to an elegant derivation of the set of states that a system can be steered to by making measurements on a remote system.

Marc-Oliver Pleinert

Lingguang Xu

Traditional physics divides classical and quantum regimes artificially, attributing microscopic imaging blur, observational uncertainty, and cosmic horizon limitation to different mechanisms: diffraction in optics, intrinsic randomness in quantum theory, and spacetime expansion in cosmology. Based on the KuiQuark Sea discrete medium axiom system, this paper establishes a unified two-scale observation barrier system covering microscopic optics and macroscopic cosmology. This paper proposes two core physical thresholds: the microscopic double observation area barrier (3×10⁻¹⁴ m² instrumental imaging limit, 10⁻²⁷ m² cosmic bare-eye ultimate limit) and the macroscopic KuiQuark light wall critical distance (10¹⁰ light-years). All microscopic fuzzy observation, unmeasurable phenomena, and the maximum observable boundary of the universe are proven to be observation system artifacts caused by discrete medium scattering and instrumental structural defects, rather than inherent laws of particles or spacetime. This work completely eliminates the artificial boundary between classical physics and quantum physics, realizing the unified interpretation of microscopic and macroscopic observational anomalies.

Andrea Aiello, Falk Töppel, Christoph Marquardt +2 more

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.