相关论文: Dialogue on Classical and Quantum between mathemat…

Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…

Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…

This is an attempt to clarify certain concepts related to a debate on the interpretation of quantum mechanics, a debate between Andrei Khrennikov on the one side and Blake Stacey and R\"udiger Schack on the other side. Central to this…

Years ago, Itamar Pitowski asked two relevant questions: Why microphysical (quantum) phenomena and classical phenomena differ in the way they do? and, what kind of explanation could qualify as a reasonable one? I argue that both questions…

A range of quantum optics experiments is discussed in which the apparatus can be modified by detector outcomes during the course of any run. Starting with a single beamsplitter network, we work our way through a series of more complex…

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of "What is quantum in quantum randomness", i.e. what is the impact of…

The study of measurements in quantum mechanics exposes many of the ways in which the quantum world is different. For example, one of the hallmarks of quantum mechanics is that observables may be incompatible, implying among other things…

The quantum theory, that we now know, arose in the process of sharp disputes between its creators. One of the results of these disputes was the emergence in recent years of fundamentally new areas of investigation and technology - quantum…

Understanding the demarcation line between classical and quantum is an important issue in modern physics. The development of such an understanding requires a clear picture of the various concurrent notions of `classicality' in quantum…

Simulation of time dynamical physical problems has been a challenge for classical computers due to their time-complexity. To demonstrate the dominance of quantum computers over classical computers in this regime, here we simulate a…

Tracing flows of information in our quantum Universe explains why we see the world as classical.

Quantum logic has been introduced by Birkhoff and von Neumann as an attempt to base the logical primitives, the propositions and the relations and operations among them, on quantum theoretical entities, and thus on the related empirical…

These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…

Whereas the entropy of any deterministic classical system described by a principle of least action is zero, one can assign a "quantum information" to quantum mechanical degree of freedom equal to Hausdorff area of the deviation from a…

In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757, 2001) have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author (American Journal of…

The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it…

This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…

To date, quantum mechanics has proven to be our most successful theoretical model. However, it is still surrounded by a "mysterious halo" that can be summarized in a simple but challenging question: Why quantum phenomena are not understood…

In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to…