A Royal Road to Quantum Theory (or Thereabouts)

@article{Wilce2016ARR,
  title={A Royal Road to Quantum Theory (or Thereabouts)},
  author={Alexander Wilce},
  journal={Entropy},
  year={2016},
  volume={20}
}
  • Alexander Wilce
  • Published 29 June 2016
  • Computer Science, Physics, Medicine, Mathematics
  • Entropy
This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together and allows some (but not too much) room for more exotic alternatives. (This is a… Expand

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2
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References

SHOWING 1-10 OF 61 REFERENCES
Four and a Half Axioms for Finite-Dimensional Quantum Probability
It is an old idea, lately out of fashion but now experiencing a revival, that quantum mechanics may best be understood, not as a physical theory with a problematic probabilistic interpretation, butExpand
Four and a Half Axioms for Finite Dimensional Quantum Mechanics
I discuss a set of strong, but probabilistically intelligible, axioms from which one can almost derive the appratus of finite dimensional quantum theory. Stated informally, these require that systemsExpand
Some Nearly Quantum Theories
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras. Subject to some reasonable constraints, we show that no such composite exists having theExpand
Conjugates, Filters and Quantum Mechanics
The Jordan structure of finite-dimensional quantum theory is derived, in a conspicuously easy way, from a few simple postulates concerning abstract probabilistic models (each defined by a set ofExpand
Local Tomography and the Jordan Structure of Quantum Theory
Using a result of H. Hanche-Olsen, we show that (subject to fairly natural constraints on what constitutes a system, and on what constitutes a composite system), orthodox finite-dimensional complexExpand
Symmetry and Composition in Probabilistic Theories
  • Alexander Wilce
  • Computer Science, Physics
  • Electron. Notes Theor. Comput. Sci.
  • 2011
TLDR
A constructive, bottom-up recipe for building probabilistic theories having strong symmetry properties, using as data any uniform enlargement of the symmetric group S(E) of any set, to a larger group G(E), in which the monoidal product is ''non-signaling''. Expand
A derivation of quantum theory from physical requirements
Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism ofExpand
Quantum Theory and Beyond: Is Entanglement Special?
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilisticExpand
Information Processing in Convex Operational Theories
TLDR
The progress to date in this second programme to abstract the essential categorical features of classical and quantum mechanics that support various information-theoretic constraints and possibilities is reviewed, and some suggestions are offered as to how to link it with the categorical semantics for quantum processes offered by Abramsky and Coecke. Expand
Quantum Theory From Five Reasonable Axioms
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace formula for calculating probabilities). In this paperExpand
...
1
2
3
4
5
...