相关论文: Alternative linear structures for classical and qu…

The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…

Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…

In previous work we have proposed a construction of quantum-like bits that could endow a large synchronizing classical system, for example of oscillators, with quantum-like function that is not compromised by decoherence. In the present…

We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…

We show how to efficiently simulate a quantum many-body system with tree structure when its entanglement is bounded for any bipartite split along an edge of the tree. This is achieved by expanding the {\em time-evolving block decimation}…

We present a complete review of the quantum-to-classical limit of open systems by means of the theory of decoherence and the use of the Weyl-Wigner-Moyal (WWM) transformation. We show that the analytical extension of the Hamiltonian…

We raise the possibility of developing a theory of constructing quantum dynamical observables independent from quantization and deriving classical dynamical observables from pure quantum mechanical consideration. We do so by giving a…

A new notion of controllability for quantum systems that takes advantage of the linear superposition of quantum states is introduced. We call such notion von Neumann controllabilty and it is shown that it is strictly weaker than the usual…

In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative formulation of classical…

A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation, and then it must be given a classical description so that the result of the measurement appears as objective reality.…

Quantum decision systems are being increasingly considered for use in artificial intelligence applications. Classical and quantum nodes can be distinguished based on certain correlations in their states. This paper investigates some…

We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a…

Gauge theories on q-deformed spaces are constructed using covariant derivatives. For this purpose a ``vielbein'' is introduced, which transforms under gauge transformations. The non-Abelian case is treated by establishing a connection to…

We formulate a general principle that supplants a Boolean \sigma-algebra of intrinsic properties of a classical system by a \sigma-complex (a union of \sigma-algebras) of extrinsic properties of a quantum system that are elicited by…

We present here a set of lecture notes on quantum thermodynamics and canonical typicality. Entanglement can be constructively used in the foundations of statistical mechanics. An alternative version of the postulate of equal a priori…

We address the issue of coupling variables which are essentially classical to variables that are quantum. Two approaches are discussed. In the first (based on collaborative work with L.Di\'osi), continuous quantum measurement theory is used…

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…

Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers $\R$. We start with the q-deformed Heisenberg algebra $\cLLq$ which is obtained by the Moyal $\ast$-deformation of the Heisenberg algebra…

In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to…

Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…