Related papers: A general framework for phase and interference
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
We investigate interference of optical fields by examining the probability distribution of photon detection. The usual description of interference patterns in terms of superposition of classical mean fields with definite phases is…
A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an…
The content of phase information of an arbitrary phase--sensitive measurement is evaluated using the maximum likelihood estimation. The phase distribution is characterized by the relative entropy--a nonlinear functional of input quantum…
In this tutorial, we introduce the basic concepts and mathematical tools needed for phase-space description of a very common class of states, whose phase properties are described by Gaussian Wigner functions: the Gaussian states. In…
We present a general formalism with the aim of describing the situation of an entity, how it is, how it reacts to experiments, how we can make statistics with it, and how it changes under the influence of the rest of the universe. Therefore…
An operational time of arrival is introduced using a realistic position and momentum measurement scheme. The phase space measurement involves the dynamics of a quantum particle probed by a measuring device. For such a measurement an…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent discipline called Quantum Cognition. These principles have been applied to…
One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the…
Quantum interference phenomena are widely viewed as posing a challenge to the classical worldview. Feynman even went so far as to proclaim that they are the only mystery and the basic peculiarity of quantum mechanics. Many have also argued…
We study the following problem: Is it possible to explain the quantum interference of probabilities in the purely corpuscular model for elementary particles? We demonstrate that (by taking into account perturbation effects of measurement…
This note is a comment on the "quantum interferometry" section of Reference [1]. It points out that the methods of that section can be applied to more general states than the ones that are discussed in Ref. [1].
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
We present a general classification of the conditions under which cognitive science, concerned e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based…
We are going to prove that the phase-space description is fundamental both in the classical and quantum physics. It is shown that many problems in statistical mechanics, quantum mechanics, quasi-classical theory and in the theory of…
The key observation about quantum reality is that it often appears as if, at some moment, the probability of a quantum event becomes a definite outcome for us. A careful analysis suggests, however, that what we perceive as a definite state…
Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…