Depolarizing Reference Devices in Generalized Probabilistic Theories

• URL: http://arxiv.org/abs/2312.12790v3
• Date: Sun, 28 Jan 2024 23:37:54 GMT
• Title: Depolarizing Reference Devices in Generalized Probabilistic Theories
• Authors: Matthew B. Weiss
• Abstract summary: QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. We show that, given any reference measurement, a set of post-measurement reference states can always be chosen to give its probability rule very form. What stands out for the QBist project from this analysis is that it is not only the pure form of the rule that must be understood normatively, but the constants within it as well.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: QBism is an interpretation of quantum theory which views quantum mechanics as standard probability theory supplemented with a few extra normative constraints. The fundamental gambit is to represent states and measurements, as well as time evolution, with respect to an informationally complete reference device. From this point of view, the Born rule appears as a coherence condition on probability assignments across several different experiments which manifests as a deformation of the law of total probability (LTP). In this work, we fully characterize those reference devices for which this deformation takes a "simplest possible" (term-wise affine) form. Working in the framework of generalized probability theories (GPTs), we show that, given any reference measurement, a set of post-measurement reference states can always be chosen to give its probability rule this very form. The essential condition is that the corresponding measure-and-prepare channel be depolarizing. We also relate our construction to Szymusiak and S{\l}omczy\'nski's recently introduced notion of morphophoricity and re-examine critically a matrix-norm-based measure of LTP deformation in light of our results. What stands out for the QBist project from this analysis is that it is not only the pure form of the Born rule that must be understood normatively, but the constants within it as well. It is they that carry the details of quantum theory.

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)
• Derivation of Standard Quantum Theory via State Discrimination [53.64687146666141]
  General Probabilistic Theories (GPTs) is a new information theoretical approach to single out standard quantum theory. We focus on the bound of the performance for an information task called state discrimination in general models. We characterize standard quantum theory out of general models in GPTs by the bound of the performance for state discrimination.
  arXiv  Detail & Related papers  (2023-07-21T00:02:11Z)
• Can QBism exist without Q? Morphophoric measurements in generalised probabilistic theories [0.7614628596146599]
  We show that the theory built on morphophoric measurements retains the chief features of the QBism approach to the basis of quantum mechanics. In particular, we demonstrate how to extend the primal equation (Urgleichung') of QBism, designed for SIC-POVMs, to the morphophoric case of GPTs.
  arXiv  Detail & Related papers  (2023-02-09T22:21:17Z)
• 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)
• Branch-counting in the Everett Interpretation of quantum mechanics [0.0]
  Well-known branch-counting rule, for realistic models of measurements, fails this test. New rule hinges on the use of decoherence theory in defining branching structure.
  arXiv  Detail & Related papers  (2022-01-16T16:50:07Z)
• Quasiprobability fluctuation theorem behind the spread of quantum information [10.640597124563614]
  We theoretically uncover the quantum fluctuation theorem behind the informational inequality. The fluctuation theorem quantitatively predicts the statistics of the underlying quantum process. We experimentally apply an interference-based method to measure the amplitudes composing the quasiprobability.
  arXiv  Detail & Related papers  (2022-01-02T17:45:50Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• 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)
• Born's rule as a quantum extension of Bayesian coherence [0.0]
  We make a conjectured representation of the Born rule which holds true if symmetric informationally complete POVMs (or SICs) exist for every finite dimensional Hilbert space. We prove that an agent who thinks they are gambling on the outcomes of measurements on a sufficiently quantum-like system, but refuses to use this form of the Born rule when placing their bets is vulnerable to a Dutch book.
  arXiv  Detail & Related papers  (2020-12-28T18:22:42Z)
• 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)
• Symmetric Informationally Complete Measurements Identify the Irreducible Difference between Classical and Quantum Systems [0.0]
  We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) with a set of linearly independent post-measurement quantum states. We prove that the representation of the Born Rule obtained from a symmetric informationally-complete measurement (or SIC) minimizes this distinction in at least two senses.
  arXiv  Detail & Related papers  (2018-05-22T16:27:27Z)

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.