Related papers: Weak value expansion of quantum operators and its …
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…
Nucleon structure functions can be observed in Deep Inelastic Scattering experiments, but it is an outstanding challenge to confront them with fully non-perturbative QCD results. For this purpose we investigate the product of…
In this paper, we analyze a function space consisting of functions for which both the function and its Fourier transform exhibit Gaussian decay together with exponential growth governed by suitable weight functions. First, we examine…
Historically, weak values have been associated with weak measurements performed on quantum systems. Over the past two decades, a series of works have shown that weak values can be determined via measurements of arbitrary strength. One such…
Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the…
The operator product expansion is used to compute the matrix elements of composite renormalized operators on the lattice. We study the product of two fundamental fields in the two-dimensional sigma-model and discuss the possible sources of…
The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
The notion of weak measurement provides a formalism for extracting information from a quantum system in the limit of vanishing disturbance to its state. Here we extend this formalism to the measurement of sequences of observables. When…
We analyze two weak random operators, initially motivated from processes in random environment. Intuitively speaking these operators are ill-defined, but using bilinear forms one can deal with them in a rigorous way. This point of view can…
Weak values of quantum observables are a powerful tool for investigating quantum phenomena. Some methods for measuring weak values in the laboratory require weak interactions and postselection, while others are deterministic, but require…
Weak measurements are a unique tool for accessing information about weakly interacting quantum systems with minimal back action. Joint weak measurements of single-particle operators with pointer states characterized by a two-dimensional…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
The well known concept, to reduce the spatio-temporal dynamics beyond instabilities of trivial states to amplitude modulated patterns, is reviewed from the point of view of a formal perturbation expansion for general dissipative partial…
We give canonical forms of selfadjoint and isometric operators on a complex vector space $U$ with scalar product given by a positive semidefinite Hermitian form, and of Hermitian forms on $U$. For an arbitrary system of semiunitary spaces…
We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor is here the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar…
In the weak measurement formalism of Y. Aharonov et al. the so-called weak value A_w of any observable A is generally a complex number. We derive a physical interpretation of its value in terms of the shift in the measurement pointer's mean…
We consider a Hilbert space that is a product of a finite number of Hilbert spaces and operators that are represented by "componental operators" acting on the Hilbert spaces that form the product space. We attribute operatorial properties…
The formalism of weak measurement in quantum mechanics has revealed profound connections between measurement theory, quantum foundations, and signal processing. In this paper, we develop a pointer-free derivation of superoscillations,…
In quantum mechanics, predictions are made by way of calculating expectation values of observables, which take the form of Hermitian operators. It is far less common to exploit non-Hermitian operators to perform measurements. Here, we show…