Born's rule as a quantum extension of Bayesian coherence
- URL: http://arxiv.org/abs/2012.14397v2
- Date: Mon, 1 Aug 2022 15:01:06 GMT
- Title: Born's rule as a quantum extension of Bayesian coherence
- Authors: John B. DeBrota, Christopher A. Fuchs, Jacques L. Pienaar, Blake C.
Stacey
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The subjective Bayesian interpretation of probability asserts that the rules
of the probability calculus follow from the normative principle of Dutch-book
coherence: A decision-making agent should not assign probabilities such that a
series of monetary transactions based on those probabilities would lead them to
expect a sure loss. Similarly, the subjective Bayesian interpretation of
quantum mechanics (QBism) asserts that the Born rule is a normative rule in
analogy to Dutch-book coherence, but with the addition of one or more
empirically based assumptions -- i.e., the "only a little more" that connects
quantum theory to the particular characteristics of the physical world. Here we
make this link explicit for 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. The key property for being sufficiently
quantum-like is that the system admits a symmetric reference measurement, but
that this measurement is not sampling any hidden variables.
Related papers
- 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) - 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) - 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) - Law of Total Probability in Quantum Theory and Its Application in
Wigner's Friend Scenario [0.0]
It is well-known that the law of total probability does not hold in general in quantum theory.
In this work, the definition of conditional probability in quantum theory is extended to POVM measurements.
Applying the theory developed here to analyze several quantum no-go theorems related to the extended Wigner's friend scenario reveals logical loopholes in these no-go theorems.
arXiv Detail & Related papers (2022-04-24T18:59:55Z) - 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) - Impossibility of creating a superposition of unknown quantum states [16.467540842571328]
We show that the existence of a protocol that superposes two unknown pure states with nonzero probability leads to violation of other no-go theorems.
Such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden in quantum theory.
arXiv Detail & Related papers (2020-11-04T13:25:42Z) - The Quantum Totalitarian Property and Exact Symmetries [0.0]
We discuss a point, which from time to time has been doubted in the literature.
All symmetries, such as those induced by the energy and momentum conservation laws, hold in quantum physics exactly.
arXiv Detail & Related papers (2020-04-30T23:16:21Z) - Improved tripartite uncertainty relation with quantum memory [5.43508370077166]
Uncertainty principle is a striking and fundamental feature in quantum mechanics.
In quantum information theory, this uncertainty principle is popularly formulized in terms of entropy.
We present an improvement of tripartite quantum-memory-assisted entropic uncertainty relation.
arXiv Detail & Related papers (2020-04-09T03:54:51Z) - 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) - Quantum-secure message authentication via blind-unforgeability [74.7729810207187]
We propose a natural definition of unforgeability against quantum adversaries called blind unforgeability.
This notion defines a function to be predictable if there exists an adversary who can use "partially blinded" access to predict values.
We show the suitability of blind unforgeability for supporting canonical constructions and reductions.
arXiv Detail & Related papers (2018-03-10T05:31:38Z)
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.