Related papers: Born Rule and Logical Inference in Quantum Mechani…
We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
We consider the problem of gambling on a quantum experiment and enforce rational behaviour by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
Traditional cognitive science rests on a foundation of classical logic and probability theory. This foundation has been seriously challenged by several findings in experimental psychology on human decision making. Meanwhile, the formalism…
We give the logical description of a new kind of quantum measurement that is a reversible operation performed by an hypothetical insider observer, or, which is the same, a quantum measurement made in a quantum space background, like the…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
We derive an analogue of the quantum total probability rule by constructing a probability theory based on paraconsistent logic. Bayesian probability theory is constructed upon classical logic and a desiderata, that is, a set of desired…
In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…
According to the Kolmogorovian Censorship Hypothesis, everything that quantum theory says about the world in the language of the quantum mechanical Hilbert space formalism is actually about relationships between ordinary relative…
Nonlinear modifications of quantum mechanics have a troubled history. They were initially studied for many promising reasons: resolving the measurement problem, testing the limits of standard quantum mechanics, and reconciling it with…
Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters),…
I tentatively suggest that the superposition principle of quantum mechanics is explicable in a mathematically natural way if it is possible to understand probability amplitudes as complex-valued logarithms. This notion is inspired by the…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
Anhomomorphic logic is a new interpretation of Quantum Theory (due to R. Sorkin). It is a histories formulation (c.f. consistent histories, quantum measure theory). In this approach, reality is a co-event, which is essentially an assignment…
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 aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…