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Quadratic Voting (QV) is a social choice mechanism that addresses the "tyranny of the majority" of one-person-one-vote mechanisms. Agents express not only their preference ordering but also their preference intensity by purchasing $x$ votes…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are…
Recent accounts of probability in the many worlds interpretation of quantum mechanics are vulnerable due to their dependence on probability theory per se. For this reason, the many worlds interpretation continues to suffer from the…
The Born rule postulates that the probability of measurement in quantum mechanics is related to the squared modulus of the wave function $\psi$. We rearrange the equation for energy eigenfunctions to define the energy as the real part of…
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…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
The Born rule may be stated mathematically as the rule that probabilities in quantum theory are expectation values of a complete orthogonal set of projection operators. This rule works for single laboratory settings in which the observer…
A non-relativistic quantum mechanical theory is proposed that combines elements of Bohmian mechanics and of Everett's "many-worlds" interpretation. The resulting theory has the advantage of resolving known issues of both theories, as well…
In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an…
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…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
This paper provides theorems aimed at shedding light on issues in the foundations of quantum mechanics. These theorems can be used to propose new interpretations to the theory, or to better understand, evaluate and improve current…
According to the subjective Bayesian interpretation of quantum theory (QBism), quantum mechanics is a tool that an agent would be wise to use when making bets about natural phenomena. In particular, the Born rule is understood to be a…
Even a century after the formulation of Quantum Mechanics (QM), the wave function collapse (WFC) remains a contentious aspect of the theory. Environment-induced decoherence has offered a partial resolution by illustrating how unitary…
Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling…
In this work we establish a novel approach to the foundations of relativistic quantum theory, which is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal…