Can QBism exist without Q? Morphophoric measurements in generalised
probabilistic theories
- URL: http://arxiv.org/abs/2302.04957v1
- Date: Thu, 9 Feb 2023 22:21:17 GMT
- Title: Can QBism exist without Q? Morphophoric measurements in generalised
probabilistic theories
- Authors: Anna Szymusiak, Wojciech S{\l}omczy\'nski
- Abstract summary: 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.
- Score: 0.7614628596146599
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In a Generalised Probabilistic Theory (GPT) equipped additionally with some
extra geometric structure we define the morphophoric measurements as those for
which the measurement map transforming states into distributions of the
measurement results is a similarity. In the quantum case, morphophoric
measurements generalise the notion of a 2-design POVM, thus in particular that
of a SIC-POVM. We show that the theory built on this class of 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. In the latter setting, the equation takes a different, albeit more
symmetric, form, but all the quantities that appear in it can be interpreted in
probabilistic and operational terms, as in the original `Urgleichung'.
Related papers
- Characterizing quantum state-space with a single quantum measurement [0.0]
We show that quantum theory can be derived from studying the behavior of a single "reference" measuring device.
In this privileged case, each quantum state correspond to a probability distribution over the outcomes of a single measurement.
We show how 3-designs allow the structure-coefficients of the Jordan algebra of observables to be extracted from the probabilities which characterize the reference measurement.
arXiv Detail & Related papers (2024-12-18T05:00:45Z) - Bit symmetry entails the symmetry of the quantum transition probability [0.0]
We show that bit symmetry implicates the symmetry of the transition probabilities between the atoms.
We conclude that bit symmetry rules out all models but the classical cases and in the simple Euclidean Jordan algebras.
arXiv Detail & Related papers (2024-11-27T18:31:45Z) - Depolarizing Reference Devices in Generalized Probabilistic Theories [0.0]
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.
arXiv Detail & Related papers (2023-12-20T06:22:55Z) - 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 state inference from coarse-grained descriptions: analysis and
an application to quantum thermodynamics [101.18253437732933]
We compare the Maximum Entropy Principle method, with the recently proposed Average Assignment Map method.
Despite the fact that the assigned descriptions respect the measured constraints, the descriptions differ in scenarios that go beyond the traditional system-environment structure.
arXiv Detail & Related papers (2022-05-16T19:42:24Z) - Theory of Quantum Generative Learning Models with Maximum Mean
Discrepancy [67.02951777522547]
We study learnability of quantum circuit Born machines (QCBMs) and quantum generative adversarial networks (QGANs)
We first analyze the generalization ability of QCBMs and identify their superiorities when the quantum devices can directly access the target distribution.
Next, we prove how the generalization error bound of QGANs depends on the employed Ansatz, the number of qudits, and input states.
arXiv Detail & Related papers (2022-05-10T08:05:59Z) - 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) - 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) - Symmetries of quantum evolutions [0.5735035463793007]
Wigner's theorem establishes that every symmetry of quantum state space must be either a unitary transformation, or an antiunitary transformation.
We show that it is impossible to extend the time reversal symmetry of unitary quantum dynamics to a symmetry of the full set of quantum evolutions.
Our no-go theorem implies that any time symmetric formulation of quantum theory must either restrict the set of the allowed evolutions, or modify the operational interpretation of quantum states and processes.
arXiv Detail & Related papers (2021-01-13T09:47:32Z) - Generalized Sliced Distances for Probability Distributions [47.543990188697734]
We introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs)
GSPMs are rooted in the generalized Radon transform and come with a unique geometric interpretation.
We consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum.
arXiv Detail & Related papers (2020-02-28T04:18:00Z) - 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.