Operational reconstruction of quantum theory
For specified operational axioms and composite-system rules, establish their independence and reconstruction power, and determine which alternative theories are experimentally distinguishable; extend controlled reconstructions beyond their finite-dimensional a
Problem statement
For specified operational axioms and composite-system rules, establish their independence and reconstruction power, and determine which alternative theories are experimentally distinguishable; extend controlled reconstructions beyond their finite-dimensional assumptions.
Lean 4
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Background
Quantum theory's mathematical apparatus — Hilbert spaces, composition, completely positive maps and outcome probabilities — is usually postulated. Reconstruction asks which operational or information-theoretic axioms select the usual quantum predictions, and which assumptions rule out physically different alternatives rather than equivalent representations.
What is known: Hardy, Chiribella–D'Ariano–Perinotti, Masanes–Müller and other reconstruction programmes derive finite-dimensional quantum theory under explicit operational axioms. Generalized probabilistic theories organize alternatives and the role of composition. These are successful conditional reconstructions; there is no mathematically defined requirement that one axiom list be uniquely compelling.
Renou et al. (2021) propose a network test distinguishing a particular real-Hilbert-space theory with specified composition and independent product-source assumptions. That paper is a theoretical proposal, not the experimental realization itself, and does not exclude every formulation using real numbers. Barrios Hita et al. (PRL, June 2026) reproduce multipartite quantum predictions using a modified real composite-system postulate. Hoffreumon–Woods (March 2026 preprint) distinguish operational independence from product-state independence and give simulation results. Neither changes the conclusion of Renou's theorem under its original assumptions.
Concrete remaining targets include independence within a fixed axiom vocabulary, compositional consistency of probability rules (the mathematical part of archived F2), infinite-dimensional reconstruction with explicit continuity assumptions, and tests separating operationally inequivalent alternatives. Distinguish alternative physics from merely changing scalar representation. Related: F1, F7, M11.
Progress & source assessment
Source catalogue review: 4 September 2026. Improved indicates partial progress, including qualified preprint claims.
published: A real-number formulation recovers multipartite predictions by modifying the composite-system postulate; this does not refute network no-go results with their original assumptions. Evidence
preprint: Operational source independence and product-state independence are distinguished in real simulations of quantum protocols. Evidence
- [1]Hardy, 'Quantum theory from five reasonable axioms' (2001) link
- [2]Chiribella, D'Ariano & Perinotti, 'Informational derivation of quantum theory', PRA 84, 012311 (2011) link
- [3]Renou et al., 'Quantum theory based on real numbers can be experimentally falsified', Nature 600 (2021) link
- [4]Barrios Hita et al., 'Quantum Mechanics Based on Real Numbers: A Consistent Description', PRL 136, 240202 (2026) link
- [5]Hoffreumon & Woods, 'Quantum theory based on real numbers cannot be experimentally falsified' (2026), preprint link
Recorded progress
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