相关论文: Games with Quantum Analogues

The measurement problem and the role of observers have plagued quantum mechanics since its conception. Attempts to resolve these have introduced anthropomorphic or non-realist notions into physics. A shift of perspective based upon process…

Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…

We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…

There are good motivations for considering some type of quantum histories formalism. Several possible formalisms are known, defined by different definitions of event and by different selection criteria for sets of histories. These…

We present a perspective on quantum games that focuses on the physical aspects of the quantities that are used to implement a game. If a game is to be played, it has to be played with objects and actions that have some physical existence.…

In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…

Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…

We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…

We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…

We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…

Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…

The true dynamical randomness is obtained as a natural fundamental property of deterministic quantum systems. It provides quantum chaos passing to the classical dynamical chaos under the ordinary semiclassical transition, which extends the…

Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…

Contrary to common belief, it is not difficult to construct deterministic models where stochastic behavior is correctly described by quantum mechanical amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What is…

The quantum mechanics of closed systems such as the universe is formulated using an extension of familiar probability theory that incorporates negative probabilities. Probabilities must be positive for sets of alternative histories that are…

A process model of quantum mechanics utilizes a combinatorial game to generate a discrete and finite causal space upon which can be defined a self-consistent quantum mechanics. An emergent space-time M and continuous wave function arise…

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly"…

We introduce a new "positive formalism" for encoding quantum theories in the general boundary formulation, somewhat analogous to the mixed state formalism of the standard formulation. This makes the probability interpretation more natural…

As described quantum mechanically, an experimental trial parses into "a preparation" expressed by a density operator and "a measurement" expressed by a set of detection operators, one for each measurable event. A density operator and a…

We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…