Reconstruction of Quantum Theory
State spaces of a two-level system in generalized probabilistic theories (GPTs), shown from left to right: the classical bit, characterized by a single parameter; the real bit, represented by a circle; the qubit, represented by the three-dimensional Bloch sphere; and, in the general GPT case, a bit represented by a d-dimensional sphere.
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Quantum theory is extraordinarily successful in its predictions, yet its interpretation remains unsettled. This has motivated the view that its meaning should be sought not only in its formalism, but also in the simple physical principles from which the theory can be derived.
Following Hardy’s seminal work, our group helped pioneer the reconstruction of quantum theory from such principles. We showed that both classical probability theory and quantum theory arise from four natural axioms concerning information capacity, equivalence of elementary systems, local tomography, and reversibility, while continuity of reversible transformations singles out the quantum case. We also showed that the structure of probabilistic theory is closely tied to the dimensionality of physical space. Under plausible assumptions of operational closure — requiring that classical laboratory devices emerge from within the theory itself in its classical limit — this approach leads uniquely to quantum theory in three-dimensional space. |
Further reading:
- B. Dakic and Č. Brukner, Quantum Theory and Beyond: Is Entanglement Special?, Contribution to “Deep beauty”, Editor Hans Halvorson (Cambridge Press, 2011).
- Č. Brukner, Questioning the rules of the game, Physics 4, 55 (2011).
- B. Dakic and Č. Brukner, The classical limit of a physical theory and the dimensionality of space, in "Quantum Theory: Informational Foundations and Foils", Eds. G. Chiribella and R. Spekkens (Fundamental Theories of Physics, Volume 181, Springer, 2016). Preprint at arXiv:1307.3984