Curator's Take
AI Commentary
This article tackles a long‑standing gap by giving an operational, theory‑independent definition of quantum superposition within the Generalised Probabilistic Theories framework, which is crucial for interpreting emerging experiments on indefinite causal order and quantum gravity that rely on “superposed” processes. By proving that only the standard quantum tensor product can consistently extend three natural superposition principles from subsystems to composites, it shows why entanglement and preparation uncertainty are not accidental quirks but inevitable consequences of a deeper superposition structure. The result both sharpens our foundational understanding of why quantum theory composes the way it does and sets clear constraints for any future post‑quantum or hybrid models that aim to go beyond Hilbert space mechanics.
— Mark Eatherly
Summary
Textbook quantum superposition refers to the feature that certain linear combinations of Hilbert space rays, each representing a valid quantum state, are themselves valid states. This notion is not operational, and it relies on the underlying Hilbert space formalism. Recent proposals for experimental tests of indefinite causal order, as well as tests probing the non-classicality of gravity, pivot on superposition, thereby calling for a theory-independent, operational formalisation of the concept. Here, we define superposition within the framework of Generalised Probabilistic Theories, based on observed statistics in prepare-and-measure experiments. Using this, we formulate three superposition principles to investigate which structural features of quantum theory carry over to other theories. We study conditions under which these principles carry over from subsystems to their compositions; to this end, we show that the quantum tensor product emerges as the largest composition rule for quantum systems respecting all three principles. Furthermore, we show how non-classical features such as entanglement and preparational uncertainty can be viewed as special forms of superposition.