Related papers: A refinement of quantum mechanics by algorithmic r…
Quantum mechanics has lacked a widely recognized interpretation since its birth. Many of these are still under consideration because interpretations are tough or impossible to disprove experimentally. We show how to distinguish…
It was repeatedly underlined in literature that quantum mechanics cannot be considered a closed theory if the Born Rule is postulated rather than derived from the first principles. In this work the Born Rule is derived from the…
The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D.Wallace has presented a formal proof of the Born rule via decision theory, as proposed by D.Deutsch. The idea is to get subjective probabilities from…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…
The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…
We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a…
Randomness is a fundamental aspect of quantum mechanics, arising from the measurement process that collapses superpositions into definite outcomes according to Born's rule. Generating large-scale random quantum states is crucial for quantum…
The partial trace is commonly introduced in quantum mechanics as an algebraic operation used to define reduced states of composite systems. However, the probabilistic origin of this operation goes systematically unnoticed in the literature.…
This tutorial is devoted to review the modern tools of quantum mechanics, which are suitable to describe states, measurements, and operations of realistic, not isolated, systems in interaction with their environment, and with any kind of…
This work introduces Algorithmic Idealism a framework that reinterprets quantum mechanics as a computational process governed by algorithmic probability informational simplicity and utility optimization Reality is modeled as an…
Randomness is fundamental in quantum theory, with many philosophical and practical implications. In this paper we discuss the concept of algorithmic randomness, which provides a quantitative method to assess the Borel normality of a given…
We suggest and describe how to analyze new types of experiments that would test a proposed model of the quantum measurement process. That model produces the Born Rule as a corollary, and so agrees with conventional quantum predictions. The…
Without Niels Bohr, QBism would be nothing. But QBism is not Bohr. This paper attempts to show that, despite a popular misconception, QBism is no minor tweak to Bohr's interpretation of quantum mechanics. It is something quite distinct.…
Algorithmic approach is based on the assumption that any quantum evolution of many particle system can be simulated on a classical computer with the polynomial time and memory cost. Algorithms play the central role here but not the…
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal…
We establish an operational rigidity result for a broad class of probability rules in infinite-dimensional settings, applicable under normality and steering assumptions. Starting from a topological generalization of generalized…