相关论文: A Quantum Model for the Ellsberg and Machina Parad…

Einstein-Podolsky-Rosen (EPR) paradox is considered in a relation to a measurement of an arbitrary quantum system . It is shown that the EPR paradox always appears in a gedanken experiment with two successively joined measuring devices.

Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…

The EPR paradox is known as an interpretive problem, as well as a technical discovery in quantum mechanics. It defined the basic features of two-quantum entanglement, as needed to study the relationships between two non-commuting variables.…

Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…

Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…

We consider a sequence of repeated interactions between an agent and an environment. Uncertainty about the environment is captured by a probability distribution over a space of hypotheses, which includes all computable functions. Given a…

Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…

The purpose of this paper is to challenge the existing paradigm on which contemporary models of generalised uncertainty relations (GURs) are based, that is, the assumption of modified commutation relations. We review an array of theoretical…

We present a very general geometrico-dynamical description of physical or more abstract entities, called the 'general tension-reduction' (GTR) model, where not only states, but also measurement-interactions can be represented, and the…

In this paper we use the framework of generalized probabilistic theories to present two sets of basic assumptions, called axioms, for which we show that they lead to the Hilbert space formulation of quantum mechanics. The key results in…

We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This…

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…

The famous Saint Petersburg Paradox (St. Petersburg Paradox) shows that the theory of expected value does not capture the real-world economics of decision-making problems. Over the years, many economic theories were developed to resolve the…

In this paper we present a solution of the Einstein's boxes paradox by modern Quantum Mechanics in which a notion of density matrix is equivalent to a notion of a quantum state of a system. We use a secondary quantization formalism in the…

The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new…

We constructed a Hilbert space representation of a contextual Kolmogorov model. This representation is based on two fundamental observables -- in the standard quantum model these are position and momentum observables. This representation…

The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…

In this paper, we demonstrate the equivalence between the complex Hilbert space and real Kahler space formulations of quantum mechanics. Complex numbers play an important role in the traditional formulation of quantum mechanics in complex…

In this work, we examine the paradox proposed by Einstein, Podolsky, and Rosen (EPR). They argued that since one may know the exact momentum of a particle without measurement and subsequently measure its position, a contradiction with the…

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts' creation-discovery view and hidden measurement approach: a fundamental explanatory…