Related papers: Linear optics implementation of weak values in Har…
We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure -- weak measurement followed by a strong one (post-selection),…
The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be…
On the torus group, on the group of p-adic integers and on the p-adic solenoid, we give a construction of an arbitrary weakly infinitely divisible probability measure using a random element with values in a product of (possibly infinitely…
In this note we give several characterisations of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the…
It is shown, that the Aharonov-Albert-Vaidman concept of weak values appears to be a consequence of a more general quantum phenomenon of weak quantum evolution. Here the concept of weak quantum evolution is introduced and discussed for the…
Post-selected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
We generalize a theorem by Titchmarsh about the mean value of Hardy's $Z$-function at the Gram points to the Hecke $L$-functions, which in turn implies the weak Gram law for them. Instead of proceeding analogously to Titchmarsh with an…
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 refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a beam as the detector for the conditioned von Neumann measurement of a system…
Weak measurements introduced by Aharonov, Albert and Vaidman (AAV) can provide informations about the system with minimal back action. Weak values of product observables (commuting) or higher moments of an observable are informationally…
Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the…
Some exact formulae of the expectation values and probability densities in a weak measurement for an operator ${\bf A}$ which satisfies the property ${\bf A}^{2}=1$ are derived. These formulae include all-order effects of the unitary…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
We generalize the concept of a weak value of a quantum observable to cover arbitrary real positive operator measures. We show that the definition is operationally meaningful in the sense that it can be understood within the quantum theory…
The problem of inferring the outcome of a simultaneous measurement of two non-commuting observables is addressed. We show that for certain pairs with dense spectra, precise inferences of the measurement outcomes are possible in pre-and…
Weak value measurements have recently given rise to a large interest for both the possibility of measurement amplification and the chance of further quantum mechanics foundations investigation. In particular, a question emerged about weak…
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 inferred from weak measurements have been proposed as a tool to investigate trajectories of pre- and post-selected quantum systems. Are the inferences drawn from the weak values about the past of a quantum particle fully true?…
Progress in testing fundamental physics relies on our ability to measure exceedingly small physical quantities. Using a $^{40}$Ca$^{+}$ trapped ion system as an example we show that an exceedingly weak synthetic magnetic field (at the scale…