A quantum prediction as a collection of epistemically restricted classical predictions

• URL: http://arxiv.org/abs/2107.02728v5
• Date: Wed, 16 Feb 2022 23:21:57 GMT
• Title: A quantum prediction as a collection of epistemically restricted classical predictions
• Authors: William F. Braasch Jr. and William K. Wootters
• Abstract summary: We show how the quantum description of an experiment can be decomposed into classical descriptions. One recovers the quantum prediction via a simple but highly nonclassical rule.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is noncontextual. In this paper we show how, for a certain class of quantum systems, the quantum description of an experiment can be decomposed into classical descriptions that are epistemically restricted, though in a different sense than in Spekkens' work. For each aspect of the experiment -- the preparation, the transformations, and the measurement -- the epistemic restriction limits the form of the probability distribution an imagined classical observer may use. There are also global constraints that the whole collection of classical descriptions must satisfy. Each classical description generates its own prediction regarding the outcome of the experiment. One recovers the quantum prediction via a simple but highly nonclassical rule: the "nonrandom part" of the predicted quantum probabilities is obtained by summing the nonrandom parts of the classically predicted probabilities. By "nonrandom part" we mean the deviation from complete randomness, that is, from what one would expect upon measuring the fully mixed state.

Related papers

• 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)
• Exploring the transition between Quantum and Classical Mechanics [0.0]
  We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. We find that the quantum probability density coincides with the classical normal distribution of the particle's final position. We propose a novel approach to recover the classical distribution from the quantum one.
  arXiv  Detail & Related papers  (2024-05-28T20:18:16Z)
• Hybrid quantum-classical systems: Quasi-free Markovian dynamics [0.0]
  In the case of a quantum-classical hybrid system, the problem of characterizing the most general dynamical semigroup is solved under the restriction of being quasi-free. We show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator valued measure and instrument. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behaviour of the quantum one.
  arXiv  Detail & Related papers  (2023-07-05T19:26:09Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• 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)
• Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality [69.62715388742298]
  We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs) We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way. We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
  arXiv  Detail & Related papers  (2022-03-08T14:47:39Z)
• Estimation independence as an axiom for quantum uncertainty [0.0]
  We show that a plausible principle of estimation independence, which requires that the estimation of momentum of one system must be independent of the position of another system, singles out the specific forms of the estimator.
  arXiv  Detail & Related papers  (2020-05-12T07:12:17Z)
• Characterization of the probabilistic models that can be embedded in quantum theory [0.0]
  We show that only classical and standard quantum theory with superselection rules can arise from a physical decoherence map. Our results have significant consequences for some experimental tests of quantum theory, by clarifying how they could (or could not) falsify it.
  arXiv  Detail & Related papers  (2020-04-13T18:09:39Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)
• 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.