Fragile Systems: A hidden variable theory for quantum mechanics

• URL: http://arxiv.org/abs/1609.01972v2
• Date: Thu, 17 Apr 2025 19:17:49 GMT
• Title: Fragile Systems: A hidden variable theory for quantum mechanics
• Authors: Yasmin Navarrete, Sergio Davis,
• Abstract summary: Quantum Mechanics is derived from the application of Bayesian probability theory to "fragile" systems.<n>Complex Hilbert spaces, non-commuting operators and the trace rule for expectations all arise naturally from the use of linear algebra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The formalism of Quantum Mechanics is derived from the application of Bayesian probability theory to "fragile" systems, i.e. systems that are perturbed by the act of measurement. Complex Hilbert spaces, non-commuting operators and the trace rule for expectations all arise naturally from the use of linear algebra to solve integral equations involving classical probabilities over hidden variables. We comment on the case of non-local hidden variables, where violations of Bell's theorem can be produced, as well as the non-fragile limit of the theory, where all measurements are commutative and the theory becomes analogous to classical statistical mechanics.

Related papers

• Probability-based approach to hybrid classical-quantum systems of any size: Generalized Gleason and Kraus theorems [0.0]
  A fully quantum effective description of hybrid classical-quantum systems is straightforward to formulate when the classical subsystem is discrete. We propose a probability-based approach starting with four axioms for hybrid classical-quantum probability measures. Explicit expressions for these transformations are derived when the classical and quantum subsystems are non-interacting.
  arXiv  Detail & Related papers  (2024-08-20T14:13:44Z)
• The probabilistic world II : Quantum mechanics from classical statistics [0.0]
  A simple neuromorphic computer based on neurons in an active or quiet state within a probabilistic environment can learn the unitary transformations of an entangled two-qubit system. Our explicit constructions constitute a proof that no-go theorems for the embedding of quantum mechanics in classical statistics are circumvented.
  arXiv  Detail & Related papers  (2024-08-09T14:02:55Z)
• Questionable and Unquestionable in Quantum Mechanics [0.0]
  We derive the basic postulates of quantum physics from a few very simple operational assumptions. We show that anything that can be described in operational terms can, if we wish, be represented in the Hilbert space quantum mechanical formalism.
  arXiv  Detail & Related papers  (2023-09-05T03:32:30Z)
• Connecting classical finite exchangeability to quantum theory [45.76759085727843]
  Exchangeability is a fundamental concept in probability theory and statistics.<n>It allows to model situations where the order of observations does not matter.<n>It is well known that both theorems do not hold for finitely exchangeable sequences.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Quantum-Classical Hybrid Systems and their Quasifree Transformations [0.0]
  We study continuous variable systems in which quantum and classical degrees of freedom are combined and treated on the same footing. This allows a unified treatment of a large variety of quantum operations involving measurements or dependence on classical parameters.
  arXiv  Detail & Related papers  (2022-08-09T19:51:10Z)
• Quantum Mechanics as a Theory of Incompatible Symmetries [77.34726150561087]
  We show how classical probability theory can be extended to include any system with incompatible variables. We show that any probabilistic system (classical or quantal) that possesses incompatible variables will show not only uncertainty, but also interference in its probability patterns.
  arXiv  Detail & Related papers  (2022-05-31T16:04:59Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• Arithmetic loophole in Bell's theorem: An overlooked threat to entangled-state quantum cryptography [0.0]
  Bell's theorem is supposed to exclude all local hidden-variable models of quantum correlations. An explicit counterexample shows that a new class of local realistic models can reconstruct rotationally symmetric quantum probabilities.
  arXiv  Detail & Related papers  (2020-04-06T16:48:41Z)
• Bell's theorem for trajectories [62.997667081978825]
  A trajectory is not an outcome of a quantum measurement, in the sense that there is no observable associated with it. We show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time.
  arXiv  Detail & Related papers  (2020-01-03T01:40:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.