Quasi-Quantization: Classical Statistical Theories with an Epistemic Restriction

  title={Quasi-Quantization: Classical Statistical Theories with an Epistemic Restriction},
  author={Robert W. Spekkens},
  journal={arXiv: Quantum Physics},
  • R. Spekkens
  • Published 17 September 2014
  • Philosophy
  • arXiv: Quantum Physics
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be prepared. This is termed an “epistemic restriction” because it implies a fundamental limit on the amount of knowledge that any observer can have about the physical state of a classical system. This article provides an overview of epistricted theories, that is… 
Geometric Quantization and Epistemically Restricted Theories
A large part of operational quantum mechanics can be reproduced from a classical statistical theory with a restriction which implies a limit on the amount of knowledge that an agent can have about an
Quantum mechanics as a calculus for estimation under epistemic restriction
Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying
Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
Non-relativistic quantum mechanics and classical statistical mechanics are derived within a common framework by an ontic nonseparable random variable and a restriction on the allowed phase space distribution, both of order Planck’s constant.
Quantum Theory is a Quasi-stochastic Process Theory
There is a long history of representing a quantum state using a quasi-probability distribution: a distribution allowing negative values. In this paper we extend such representations to deal with
Classical theories with entanglement
We investigate operational probabilistic theories where the pure states of every system are the vertices of a simplex. A special case of such theories is that of classical theories, i.e. simplicial
“The Heisenberg Method”: Geometry, Algebra, and Probability in Quantum Theory
The article explores the implications of the Heisenberg method and of the QPA principle for quantum theory, and for the relationships between mathematics and physics there, from a nonrealist or, in terms of this article, “reality-without-realism” or RWR perspective, defining the RWR principle.
Classicality without local discriminability: Decoupling entanglement and complementarity
It is demonstrated that the presence of entanglement is independent of the existence of incompatible measurements, and on the basis of the fact that every separable state of the theory is a statistical mixture of entangled states, a no-go conjecture is formulated for theexistence of a local-realistic ontological model.
On Generalised Statistical Equilibrium and Discrete Quantum Gravity
Statistical equilibrium configurations are important in the physics of macroscopic systems with a large number of constituent degrees of freedom. They are expected to be crucial also in discrete
Non-classicality as a computational resource
This thesis complete Spekkens' toy theory with measurement update rules and a mathematical framework that generalises it to systems of any finite dimensions (prime and non-prime) and extends the operational equivalence between the toy theory and stabilizer quantum mechanics to all odd dimensions via Gross' Wigner functions.
A consolidating review of Spekkens' toy theory
In order to better understand a complex theory like quantum mechanics, it is sometimes useful to take a step back and create alternative theories, with more intuitive foundations, and examine which


Reconstruction of Gaussian quantum mechanics from Liouville mechanics with an epistemic restriction
How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in
Towards a formulation of quantum theory as a causally neutral theory of Bayesian inference
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in
Information processing in generalized probabilistic theories
A framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others, is introduced, and a tensor product rule for combining separate systems can be derived.
Quantum probabilities as Bayesian probabilities
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that,
Quantum-Bayesian Coherence
It is argued that the Born Rule should be seen as an empirical addition to Bayesian reasoning itself, and how to view it as a normative rule in addition to usual Dutch-book coherence is shown.
The Problem of Hidden Variables in Quantum Mechanics
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure
Phase Groups and the Origin of Non-locality for Qubits
On the Einstein-Podolsky-Rosen Paradox
Theories of systems with limited information content
A hierarchical classification of theories that describe systems with fundamentally limited information content is introduced and it is shown that they can be ordered according to the number of mutually complementary measurements, which is also shown to define their computational abilities.
Quantum entanglement
All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism— entanglement,