Related papers: On the consistency of the quantum-like representat…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework…
Two related problems in relativistic quantum mechanics, the apparent superluminal propagation of initially localized particles and dependence of spatial localization on the motion of the observer, are analyzed in the context of Dirac's…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
We establish a new perturbation theory for orthogonal polynomials using a Riemann--Hilbert approach and consider applications in numerical linear algebra and random matrix theory. This new approach shows that the orthogonal polynomials with…
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a…
We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…
Quantum coherence is a fundamental issue in quantum mechanics and quantum information processing. We explore the coherence dynamics of the evolved states in HHL quantum algorithm for solving the linear system of equation…
A formalism for quantum error correction based on operator algebras was introduced in [1] via consideration of the Heisenberg picture for quantum dynamics. The resulting theory allows for the correction of hybrid quantum-classical…
Einstein, Podolsky and Rosen (EPR) showed that it is possible to predict with certainty the value of a property without disturbing the object in question. In contrast, Quantum Mechanics (QM) holds that if different measurement setups cannot…
A quantum lattice representation (QLA) is devised for the initial value problem of one-dimensional (1D) propagation of an electromagnetic disturbance in a scalar dielectric medium satisfying directly only the two curl equations of Maxwell.…
We introduce parabolic induction and restriction functors for rational Cherednik algebras, and study their basic properties. Then we discuss applications of these functors to representation theory of rational Cherednik algebras. In…
The Lie algebra gl(lambda) dependent on the complex parameter lambda is a continuous version of the Lie algebra gl(inf) of infinite matrices with only finite number of nonzero entries. The gl(lambda) was first introduced by B.L.Feigin in…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology.…
We clarify the role of the Born rule in the Copenhagen Interpretation of quantum mechanics by deriving it from Bohr's doctrine of classical concepts, translated into the following mathematical statement: a quantum system described by a…
Unitary representations of kinematical symmetry groups of quantum systems are fundamental in quantum theory. We propose in this paper its generalization to quantum kinematical groups. Using the method, proposed by us in a recent paper…
Lorentz covariance imposed upon a quantum logic of local propositions for which all observers can consistently maintain state collapse descriptions, implies a condition on space-like separated propositions that if imposed on generally…
This paper presents quasilinear theory (QLT) for classical plasma interacting with inhomogeneous turbulence. The particle Hamiltonian is kept general; for example, relativistic, electromagnetic, and gravitational effects are subsumed. A…