相关论文: Quantum stochastic convolution cocycles

In this article we consider the Levy processes and the corresponding semigroup. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the…

Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, when understood as a resource for quantum…

Contextuality is a fundamental non-classical property of quantum theory, which has recently been proven to be a key resource for achieving quantum speed-ups in some leading models of quantum computation. However, which of the forms of…

Semigroups describing the time evolution of open quantum systems in finite dimensional spaces have generators of a special form, known as Lindblad generators. The simple generators, characterized by only one operator, are analyzed. The…

The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed).…

Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…

In a companion paper we derived a unique time-reversal-invariant stochastic generalization of the Liouville equation and showed that it coincides with the evolution equation for the Husimi $Q$-function in a broad class of bosonic quantum…

The recent analysis on noncommutative geometry, showing quantization of the volume for the Riemannian manifold entering the geometry, can support a view of quantum mechanics as arising by a stochastic process on it. A class of stochastic…

This thesis focuses on the Lie-theoretic foundations of controlled open quantum systems. We describe Markovian open quantum system evolutions by Lie semigroups, whose corresponding infinitesimal generators lie in a special type of convex…

In a pre-selected Hilbert space of quantum states the unitarity of the evolution is usually guaranteed via a pre-selection of the generator (i.e., of the Hamiltonian operator) in self-adjoint form. In fact, the simultaneous use of both of…

This article sets out the framework of algebraic quantum field theory in curved spacetimes, based on the idea of local covariance. In this framework, a quantum field theory is modelled by a functor from a category of spacetimes to a…

Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of $sl(2)$ generators. It enables us to use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states (GCS)…

We provide a precise definition and analysis of quantum causal histories (QCH). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum…

In order to construct solutions of the braid equation we consider bijective left non-degenerate set-theoretic type solutions, which correspond to regular q-cycle coalgebras. We obtain a partial classification of the different q-cycle…

Two new approaches to the infinitesimal characterisation of quantum stochastic cocycles are reviewed. The first concerns mapping cocycles on an operator space and demonstrates the role of H\"older continuity; the second concerns contraction…

In this paper we study systematically the Euclidean renormalization in configuration spaces. We investigate also the deviation from commutativity of the renormalization and the action of all linear partial differential operators. This…

The general idea of a stochastic gauge representation is introduced and compared with more traditional phase-space expansions, like the Wigner expansion. Stochastic gauges can be used to obtain an infinite class of positive-definite…

Multiple Schramm-Loewner Evolutions (SLE) are conformally invariant random processes of several curves, whose construction by growth processes relies on partition functions: M\"obius covariant solutions to a system of second order partial…

We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…