Related papers: Quantum-Bayesian Coherence
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement…
We argue that measurement data in quantum physics can be rigorously interpreted only as a result of a statistical, macroscopic process, taking into account the indistinguishable character of identical particles. Quantum determinism is in…
Left on its own, a quantum state evolves deterministically under the Schr\"odinger Equation, forming superpositions. Upon measurement, however, a stochastic process governed by the Born rule collapses it to a single outcome. This dual…
I argue that Bohmian mechanics (or any similar pilot-wave theory) cannot reasonably be claimed to be a deterministic theory. If one assumes the "quantum equilibrium distribution" provided by the wave function of the universe, Bohmian…
We propose a simple abstract formalisation of the act of observation, in which the system and the observer are assumed to be in a pure state and their interaction deterministically changes the states such that the outcome can be read from…
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the…
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
The author summarizes the Quantum Bayesian viewpoint of quantum mechanics, developed originally by C. M. Caves, R. Schack, and himself. It is a view crucially dependent upon the tools of quantum information theory. Work at the Perimeter…
Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
We provide a derivation of the Born Rule in the context of the Everett (Many-Worlds) approach to quantum mechanics. Our argument is based on the idea of self-locating uncertainty: in the period between the wave function branching via…
Details of the contents and the formulations of the Born rule changed considerably from its inception by Born in 1926 to the present day. This paper traces the early history of the Born rule 100 years ago, its generalization (essential for…
Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations…
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…
The argument of environment-assisted invariance (known as envariance) implying Born's rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
Bayes' rule $\mathbb{P}(B|A)\mathbb{P}(A)=\mathbb{P}(A|B)\mathbb{P}(B)$ is one of the simplest yet most profound, ubiquitous, and far-reaching results of classical probability theory, with applications in any field utilizing statistical…
A simple proof is given that the probabilities of observations in a large universe are not given directly by Born's rule as the expectation values of projection operators in a global quantum state of the entire universe. An alternative…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…