Properties of the frequency operator do not imply the quantum probability postulate

  title={Properties of the frequency operator do not imply the quantum probability postulate},
  author={Carlton M. Caves and R. Schack},
  journal={Annals of Physics},
Derivation of the quantum probability rule without the frequency operator
We present an alternative frequentists' proof of the quantum probability rule which does not make use of the frequency operator, with expectation that this can circumvent the recent criticism against
Indeterminate Probabilities and the Weak Quantum Law of Large Numbers
The quantum probabilistic convergence in measurement, distinct from mathematical convergence, is derived for indeterminate probabilities from the weak quantum law of large numbers. This is presented
Born Rule and Finkelstein-Hartle Frequency Operator Revisited
Character of observables in classical physics and quantum theory is reflected upon. Born rule in the context of measurement being an interaction between two quantum systems is discussed. A
The Limits of Quantum Mechanics in the Light of the Genuine Fortuitousness Principle
To test the limits of quantum mechanics, a proposal for an experiment on protons is suggested. The spin component of proton is measured very rapidly in sequential measurements. The reason for this
Physical origin of quantum nonlocality and contextuality
We prove that in a universe in which there are no laws governing the outcomes of some measurements and in which, as a consequence, every behavior that is not forbidden in a physical theory does take
Born Rule and its Interpretation
The Born rule provides a link between the mathematical formalism of quantum theory and experiment, and as such is almost single-handedly responsible for practically all predictions of quantum
Explanation, Evolution and Subjective Probability in Everett Quantum Mechanics with Positive Preclusion
The usual interpretational rule of quantum mechanics which states that outcomes do not occur when their weights are zero is changed so as to preclude outcomes with weights less than a small but
The Born rule as a statistics of quantum micro-events
  • Y. Brezhnev
  • Physics
    Proceedings of the Royal Society A
  • 2020
We deduce the Born rule from a purely statistical take on quantum theory within minimalistic math-setup. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics—a
Emergence of outcomes in quantum mechanics
A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the


On the probabilistic postulate of quantum mechanics
We study whether the probabilistic postulate could be derived from basic principles. Through the analysis of the Strong Law of Large Numbers and its formulation in quantum mechanics, we show,
Using classical probability to guarantee properties of infinite quantum sequences.
  • Gutmann
  • Mathematics
    Physical review. A, Atomic, molecular, and optical physics
  • 1995
A nonprobabilistic quantum analogue to the law of large numbers, the randomness property, and all other familiar almost-sure theorems of classical probability is obtained.
Quantum Mechanics of Individual Systems
A discussion of the meaning of the “state” of an individual quantum mechanical system is given, and an application is made to the clarification of some of the paradoxical features of the theory.
Quantum mechanics
Quantum Mechanics for Organic Chemists.By Howard E. Zimmerman. Pp. x + 215. (Academic: New York and London, May 1975.) $16.50; £7.90.
Characterizing Quantum Theory in Terms of Information-Theoretic Constraints
We show that three fundamental information-theoretic constraints—the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the
Quantum Mechanics is About Quantum Information
I argue that quantum mechanics is fundamentally a theory about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles. The notion of
Quantum Theory from Four of Hardy's Axioms
In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of “quantum theory from five reasonable axioms.” Here we show that Hardy's first axiom, which identifies probability with
Unknown Quantum States: The Quantum de Finetti Representation
We present an elementary proof of the quantum de Finetti representation theorem, a quantum analog of de Finetti’s classical theorem on exchangeable probability assignments. This contrasts with the