2021/07/31 by William F. Braasch, William F. Braasch Jr., William K. Wootters
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Artificial intelligence #Class (philosophy) #Classical physics #Computer science #Epistemology #Mathematics #Observer (physics) #Phase space #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum dynamics #Quantum mechanics #Quantum probability #Quantum process #Randomness #Simple (philosophy) #Statistical physics #Statistics #quant-ph
paper · pdf · doi:10.22331/q-2022-02-21-659
published as Quantum 6, 659 (2022) · 28 pages, 3 figures; revised title, introduction, and Figure 2 in v2; minor corrections and changes to notation in v3; v4 is the version accepted in Quantum; appendices changed in v5
openalex created_date 2021/07/19 · arxiv created 2022/02/16 · openalex publication_date 2022/02/21 · arxiv updated 2022/03/09 · openalex updated_date 2026/08/05
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is noncontextual. In this paper we show how, for a certain class of quantum systems, the quantum description of an experiment can be decomposed into classical descriptions that are epistemically restricted, though in a different sense than in Spekkens' work. For each aspect of the experiment -- the preparation, the transformations, and the measurement -- the epistemic restriction limits the form of the probability distribution an imagined classical observer may use. There are also global constraints that the whole collection of classical descriptions must satisfy. Each classical description generates its own prediction regarding the outcome of the experiment. One recovers the quantum prediction via a simple but highly nonclassical rule: the "nonrandom part" of the predicted quantum probabilities is obtained by summing the nonrandom parts of the classically predicted probabilities. By "nonrandom part" we mean the deviation from complete randomness, that is, from what one would expect upon measuring the fully mixed state.