Related papers: Constructor Theory of Probability
The subjective Bayesian interpretation of probability asserts that the rules of the probability calculus follow from the normative principle of Dutch-book coherence: A decision-making agent should not assign probabilities such that a series…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
The quantum theory of decoherence plays an important role in a pragmatist interpretation of quantum theory. It governs the descriptive content of claims about values of physical magnitudes and offers advice on when to use quantum…
One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces.…
Recent developments in the mathematical foundations of quantum mechanics have brought the theory closer to that of classical probability and statistics. On the other hand, the unique character of quantum physics sets many of the questions…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
The origin of non-classical correlations is difficult to identify since the uncertainty principle requires that information obtained about one observable invariably results in the disturbance of any other non-commuting observable. Here,…
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…
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…
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…
We introduce a 'uniform tension-reduction' (UTR) model, which allows to represent the probabilities associated with an arbitrary measurement situation and use it to explain the emergence of quantum probabilities (the Born rule) as 'uniform'…
We provide a systematic, thorough treatment of the foundations of probability theory and stochastic processes along the lines of E. Bishop's constructive analysis. Every existence result presented shall be a construction; and the input…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
What does it take for real-deterministic c-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of real-deterministic c-valued variables out of the weak values…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
Quantum theory provides a significant example of two intermingling hallmarks of science: the ability to consistently combine physical systems and study them compositely, and the power to extract predictions in the form of correlations. A…
I provide a simple derivation of the Born rule as giving a classical probability, that is, the ratio of the measure of favorable states of the system to the measure of its total possible states. In classical systems, the probability is due…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…