Related papers: Decision Theory with a Hilbert Space as Possibilit…
The research on human cognition has recently benefited from the use of the mathematical formalism of quantum theory in Hilbert space. However, cognitive situations exist which indicate that the Hilbert space structure, and the associated…
We consider the following model of decision-making by cognitive systems. We present an algorithm -- quantum-like representation algorithm (QLRA) -- which provides a possibility to represent probabilistic data of any origin by complex…
Quantum mechanics of unitary systems is considered in quasi-Hermitian representation. In this framework the concept of perturbation is found counterintuitive, for three reasons. The first one is that in this formalism we are allowed to…
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space,…
Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space…
A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results…
In this paper we investigate the potential for persuasion arising from the quantum indeterminacy of a decision-maker's beliefs, a feature that has been proposed as a formal expression of well-known cognitive limitations. We focus on a…
We present the elements of a new approach to the foundations of quantum theory and probability theory which is based on the algebraic approach to integration, information geometry, and maximum relative entropy methods. It enables us to deal…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
We study de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants"…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
The definition of a quantum system requires a Hilbert space, a way to define the dynamics, and an algebra of observables. The structure of the observable algebra is related to a tensor product decomposition of the Hilbert space and…
This paper introduces several new classes of mathematical structures that have close connections with physics and with the theory of dynamical systems. The most general of these structures, called indivisible stochastic processes,…
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. In particular, a local quantum field theory is presented which is a supersymmetric classical model. -- The Hilbert space approach of Koopman…
Determining the physical Hilbert space is often considered the most difficult but crucial part of completing the quantization of a constrained system. In such a situation it can be more economical to use effective constraint methods, which…
We develop a kind of quantum formalism (Hilbert space probabilistic calculus) for measurements performed over cognitive (in particular, conscious) systems. By using this formalism we could predict averages of cognitive observables.…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…