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The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields,…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
How much information do we need about a process' past to faithfully simulate its future? The statistical complexity is a prominent quantifier of structure for stochastic processes. Quantum machines, however, can simulate classical…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
We reconsider the problem of the interpretation of the Quantum Theory (QT) in the perspective of the entire universe and of Bphr idea that the classical language is the language of our experience and QT acquires a meaning only with a…
Education in statistics, the application of statistics in scientific research, and statistics itself as a scientific discipline are in crisis. Within science, the main cause of the crisis is the insufficiently clarified concept of…
A significant part of quantum theory can be obtained from a single innovation relative to classical theories, namely, that there is a fundamental restriction on the sorts of statistical distributions over physical states that can be…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
In this paper we suggest a simple mathematical procedure to derive the classical probability density of quantum systems via Bohr's correspondence principle. Using Fourier expansions for the classical and quantum distributions, we assume…
We investigate probabilistic transformations of quantum states from a `source' set to a `target' set of states. Such transforms have many applications. They can be used for tasks which include state-dependent cloning or quantum state…
Communication scenarios between two parties can be implemented by first encoding messages into some states of a physical system which acts as the physical medium of the communication and then decoding the messages by measuring the state of…
Quantum theory can be regarded as a non-commutative generalization of classical probability. From this point of view, one expects quantum dynamics to be analogous to classical conditional probabilities. In this paper, a variant of the…
We remark that the often ignored quantum probability current is fundamental for a genuine understanding of scattering phenomena and, in particular, for the statistics of the time and position of the first exit of a quantum particle from a…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one,…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
Probabilistic abstract interpretation is a theory used to extract particular properties of a computer program when it is infeasible to test every single inputs. In this paper we apply the theory on neural networks for the same purpose: to…
In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so…