Intermediate determinism in general probabilistic theories

• URL: http://arxiv.org/abs/2203.14997v1
• Date: Mon, 28 Mar 2022 18:05:41 GMT
• Title: Intermediate determinism in general probabilistic theories
• Authors: Victoria J Wright
• Abstract summary: We call this feature intermediate determinism. In dimensions of at least three, the intermediate determinism of quantum theory is guaranteed by the structure of its lattice of properties. We show that, although related, both the no-restriction hypothesis and a Gleason-type theorem are neither necessary nor sufficient for intermediate determinism.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully determine the probability of finding the system to have any other property. We call this feature intermediate determinism. In dimensions of at least three, the intermediate determinism of quantum theory is guaranteed by the structure of its lattice of properties. This observation follows from Gleason's theorem, which is why it fails to hold in dimension two. In this work we extend the idea of intermediate determinism from properties to measurements. Under this extension intermediate determinism follows from the structure of quantum effects for separable Hilbert spaces of any dimension, including dimension two. Then, we find necessary and sufficient conditions for a general probabilistic theory to obey intermediate determinism. We show that, although related, both the no-restriction hypothesis and a Gleason-type theorem are neither necessary nor sufficient for intermediate determinism.

Related papers

• Testing trajectory-based determinism via time probability distributions [44.99833362998488]
  Bohmian mechanics (BM) has inherited more predictive power than quantum mechanics (QM) We introduce a prescription for constructing a flight-time probability distribution within generic trajectory-equipped theories. We derive probability distributions that are unreachable by QM.
  arXiv  Detail & Related papers  (2024-04-15T11:36:38Z)
• Internal causality breaking and emergence of entanglement in the quantum realm [1.1970409518725493]
  We investigate the quantum dynamics of two photonic modes coupled to each other through a beam splitting. We find that when the initial wave function of one mode is different from a wave packet obeying the minimum Heisenberg uncertainty, the causality in the time-evolution of each mode is internally broken.
  arXiv  Detail & Related papers  (2024-03-14T13:16:00Z)
• Connecting classical finite exchangeability to quantum theory [69.62715388742298]
  Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• A Measure-Theoretic Axiomatisation of Causality [55.6970314129444]
  We argue in favour of taking Kolmogorov's measure-theoretic axiomatisation of probability as the starting point towards an axiomatisation of causality. Our proposed framework is rigorously grounded in measure theory, but it also sheds light on long-standing limitations of existing frameworks.
  arXiv  Detail & Related papers  (2023-05-19T13:15:48Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Quantum realism: axiomatization and quantification [77.34726150561087]
  We build an axiomatization for quantum realism -- a notion of realism compatible with quantum theory. We explicitly construct some classes of entropic quantifiers that are shown to satisfy almost all of the proposed axioms.
  arXiv  Detail & Related papers  (2021-10-10T18:08:42Z)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Gentle Measurement as a Principle of Quantum Theory [9.137554315375919]
  We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. We show, within the framework of general probabilistic theories, that GMP imposes strong restrictions on the law of physics.
  arXiv  Detail & Related papers  (2021-03-28T11:59:49Z)
• Is the standard quantum mechanics a completely nondeterministic theory? [0.0]
  It is argued that although quantum theory isn't an absolutely deterministic theory, it is partially deterministic. The argument is based on the conceptual meaning of determinism and by means of some well-known phenomena in the quantum world.
  arXiv  Detail & Related papers  (2020-07-04T14:48:13Z)
• Resource theory of quantum coherence with probabilistically non-distinguishable pointers and corresponding wave-particle duality [0.6882042556551611]
  We study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors. We identify a class of measures of the quantum coherence, and in particular establish a monotonicity property of the measures. We report a relation between quantum coherence and path complementary distinguishability in a double-slit set-up.
  arXiv  Detail & Related papers  (2020-05-17T16:56:31Z)
• Indeterminism and Undecidability [0.0]
  Chaitin's follow-up to Goedel's (first) incompleteness theorem can be proved. The main point is that Bell and others did not exploit the full empirical content of quantum mechanics.
  arXiv  Detail & Related papers  (2020-03-07T11:06:23Z)

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.