Related papers: Quantum Probability from Subjective Likelihood: im…
The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's…
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 in three theorems. The first establishes…
The existence of probability in the sense of the frequency interpretation, i.e. probability as "long term relative frequency," is shown to follow from the dynamics and the interpretational rules of Everett quantum mechanics in the…
I discuss the meaning of probability in the Everett-Wheeler interpretation of quantum mechanics, together with the problem of defining histories. To resolve these, I propose an understanding of probability arising from a form of temporal…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In…
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of…
This note is sketching a simple and natural mathematical construction for explaining the probabilistic nature of quantum mechanics. It employs nonstandard analysis and is based on Feynman's interpretation of the Heisenberg uncertainty…
One more derivation of the quantum probability rule is presented in order to shed more light on the versatile aspects of this fundamental law. It is shown that the change of state in minimal quantum non-demolition measurement, also known as…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…
We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…
The problem of interpreting quantum theory on a large (e.g. cosmological) scale has been commonly conceived as a search for objective reality in a framework that is fundamentally probabilistic. The Everett programme attempts to evade the…
Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the…
In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…
I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as…
The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…