Related papers: Weak containment of measure preserving group actio…
We investigate the estimation of a small interaction parameter from the outcomes of weak quantum measurements implemented by the interaction. The relation of weak values and sensitivity is explained and the different contributions of…
We study combinations of risk measures under no restrictive assumption on the set of alternatives. We develop and discuss results regarding the preservation of properties and acceptance sets for the combinations of risk measures. One of the…
The arrival time probability distribution is defined by analogy with the classical mechanics. The difficulty of requirement to have the values of non-commuting operators is circumvented using the concept of weak measurements. The proposed…
It is well known that besides oscillations, sequences bounded only in $L^1$ can also develop concentrations, and if the latter occurs, we can at most hope for weak$^*$ convergence in the sense of measures. Here we derive a new tool to…
We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can…
We propose to use weak measurements away from the weak-value amplification regime to carry out precision measurements of time delays of light. Our scheme is robust to several sources of noise that are shown to only limit the relative…
We develop a convergent variational perturbation theory for conditional probability densities of Markov processes. The power of the theory is illustrated by applying it to the diffusion of a particle in an anharmonic potential.
Three recent results on weak measurements are presented. They are: i) repeated measurements on a single copy can not provide any information on it and further, that in the limit of very large such measurements, weak measurements have…
Sufficient conditions for the controllability of a conservative reduced system are given. Several examples illustrating the theory are also presented.
A large literature has grown up around the proposed use of 'weak measurements' (i.e., unsharp measurements followed by post-selection) to allegedly provide information about hidden ontological features of quantum systems. This paper…
Weak values arise in quantum theory when the result of a weak measurement is conditioned on a subsequent strong measurement. The majority of the trials are discarded, leaving only very few successful events. Intriguingly those can display a…
Necessary and sufficient conditions for weak and vague convergence of measures are important for a diverse host of applications. This paper aims to give a comprehensive description of the relationship between the two modes of convergence…
We build on work of Elek and Zucker and develop a topological analogue of the theory of weak containment. We show that definitions in terms of local patterns, containment in ultra(co)products, and continuous model theory are all equivalent,…
We introduce a topology on the space of actions modulo weak equivalence finer than the one previously studied in the literature. We show that the product of actions is a continuous operation with respect to this topology, so that the space…
In this paper we propose a construction of measure preserving actions of the group $R^d$ with Lebesgue spectrum of multiplicity one.
We develop a theory of twisted actions of categorical groups using a notion of semidirect product of categories. We work through numerous examples to demonstrate the power of these notions. Turning to representations, which are actions that…
We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…
Weak amplification is a signal enhancement technique which is used to measure tiny changes that otherwise cannot be determined because of technical limitations. It is based on the existence of a special type of interaction which couples a…
In this, partly pedagogical review, I attempt to give a self-contained overview of the basis of (non-relativistic) QM measurement theory expressed in density matrix formalism. The focus is on applications to the theory of weak measurement,…
The concept of (stable) weak containment for measure-preserving actions of a countable group $\Gamma$ is analogous to the classical notion of (stable) weak containment of unitary representations. If $\Gamma$ is amenable then the Rokhlin…