相关论文: Histories Approach to Quantum Mechanics
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
In this survey, we relate frame theory and quantum information theory, focusing on quantum 2-designs. These are arrangements of weighted subspaces which are in a specific sense optimal for quantum state tomography. After a brief…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely…
In this research notebook in the four-part, quantum computation and applications, quantum computation and algorithms, quantum communication protocol, and universal quantum computation for quantum engineers, researchers, and scientists, we…
Quantum information is an emerging field which has attracted a lot of attention in the last fifteen years or so. It is a broad subject which covers from the most applied questions (e.g., how to build quantum computers or secure…
We bring together two topics (quantum mechanics and time passage) with the goal of clarifying questions about each. Specifically, we claim that the formalism of quantum mechanics provides an answer to the question: "What is time passage?".
From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…
We provide an introduction to the theory of quantum measurements that is centered on the pivotal role played by John von Neumann's model. This introduction is accessible to students and researchers from outside the field of foundations of…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
Based on the assumption that time evolves only in one direction and mechanical systems can be described by Lagrangeans, a dynamical C*-algebra is presented for non-relativistic particles at atomic scales. Without presupposing any…