Related papers: Filtering of Wide Sense Stationary Quantum Stochas…
Recent developments in quantum technology mean that is it now possible to manipulate systems and measure fermion fields (e.g. reservoirs of electrons) at the quantum level. This progress has motivated some recent work on filtering theory…
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,…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Quantum computing is usually associated with discrete quantum states and physical quantities possessing discrete eigenvalue spectrum. However, quantum computing in general is any computation accomplished by the exploitation of quantum…
Measurements continuous in time were consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after the…
The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in…
"Quantum sensing" describes the use of a quantum system, quantum properties or quantum phenomena to perform a measurement of a physical quantity. Historical examples of quantum sensors include magnetometers based on superconducting quantum…
This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the…
It is well known that the spectrum condition, i.e. the positivity of the energy in every inertial coordinate system, is one of the central conceptual ingredients in model-independent approaches to relativistic quantum field theory. When one…
A new idea for the quantization of dynamic systems, as well as space time itself, using a stochastic metric is proposed. The quantum mechanics of a mass point is constructed on a space time manifold using a stochastic metric. A stochastic…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
Quantum sensors allow the estimation of parameters with precision higher than that obtained with classical strategies. Devices based on quantum physics have allowed the precise estimation of the gravitational field, the detailed imaging of…
We show how the concept of quantum open system and the methods in non-equilibrium statistical mechanics can be usefully applied to studies of quantum statistical processes in the early universe. We first sketch how noise, fluctuation,…
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite…
Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic…
In this communication, we propose a tentative to set the fundamental problem of measuring process done by a large structure on a microsopic one. We consider the example of voting when an entire society tries to measure globally opinions of…
We develop a prequantum classical statistical model in that the role of hidden variables is played by classical (vector) fields. We call this model Prequantum Classical Statistical Field Theory (PCSFT). The correspondence between classical…
Classification, the computational process of categorizing an input into pre-existing classes, is now a cornerstone in modern computation in the era of machine learning. Here we propose a new type of quantum classifier, based on quantum…
Beginning in abstract space and dislodging the representational form paves a way to formulate a version of a quantum physical measurement scheme. With materiality playing sustainment roles with respect to q-states, these latter control…