Related papers: Sequential Quantum Measurements and the Instrument…
A time inhomogeneous generalized Mehler semigroup on a real separable Hilbert space ${\mathds{H}}$ is defined through $$ p_{s,t}f(x)=\int_{\mathds{H}} f(U(t,s)x+y)\,\mu_{t,s}(dy), \quad t\geq s, \ x\in{\mathds{H}} $$ for every bounded…
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…
We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the…
The notion of a coalgebra measuring, introduced by Sweedler, is a kind of generalized ring map between algebras. We begin by studying maps on Hochschild homology induced by coalgebra measurings. We then introduce a notion of coalgebra…
This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. Section~1 reviews the…
Quantum instruments are mathematical devices introduced to describe the conditional state change during a quantum process. They are completely positive map valued measures on measurable spaces. We may also view them as non-commutative…
Recent advances in nanotechnology have enabled researchers to manipulate small collections of quantum mechanical objects with unprecedented accuracy. In semiconductor quantum dot qubits, this manipulation requires controlling the dot…
We study the effects of decoherence in the form of optical phase diffusion, photon loss and gain, and atomic dephasing in entangled atomic ensembles produced via quantum nondemolition (QND) measurements. For the optical decoherence…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
A long-standing problem in quantum mesoscopic physics is which operator order corresponds to noise expressions like <I(-\omega)I(\omega)>, where I(\omega) is the measured current at frequency \omega. Symmetrized order describes a classical…
We prove that the algebra $\mI_n:=K\langle x_1, ..., x_n, \frac{\der}{\der x_1},...,\frac{\der}{\der x_n}, \int_1, ..., \int_n\rangle $ of integro-differential operators on a polynomial algebra is a prime, central, catenary, self-dual,…
Contrary to conventional quantum mechanics, which treats measurement as instantaneous, here we explore a model for finite-time measurement. The main two-level system interacts with the measurement apparatus in a Markovian way described by…
In previous papers we have explained how a sequence of theorems by John von Neumann on infinite tensor products (ITP) can be understood as providing elements to support both sectorisation of the Hilbert space of large quantum systems, and a…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$…
A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement apparatus is modeled as an ideal Bose gas, the…
Simultaneous measurement of several noncommuting observables is modeled by using semigroups of completely positive maps on an algebra with a non-trivial center. The resulting piecewise-deterministic dynamics leads to chaos and to nonlinear…
The discrete spatial geometry underlying Loop Quantum Gravity (LQG) is degenerate almost everywhere. This is at apparent odds with the non- degeneracy of asymptotically flat metrics near spatial infinity. Koslowski generalised the LQG…