Related papers: Comment on "Weak value amplification is suboptimal…
In this review we present some recent extensions of the method of the weakly conjugate operator. We illustrate these developments through examples of operators on graphs and groups.
The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…
Given $n$ independent and identically distributed observations and measuring the value of obtaining an additional observation in terms of Le Cam's notion of deficiency between experiments, we show for certain types of non-parametric…
The technique of weak value amplification, proposed by Aharonov et al. in 1988, has been applied for various fields of physics for the purpose of precision measurement, which is made possible by exploiting the freedom of `postselection'…
Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We…
The weak value of an observable is experimentally accessible by weak measurements as theoretically analyzed by Aharonov et al. and recently experimentally demonstrated. We introduce a weak operator associated with the weak values and give a…
We consider several weak type estimates for singular operators using the Bellman function approach. We disprove the $A_1$ conjecture of Muckenhoupt, which stayed open after Muckenhoupt--Wheeden's conjecture was disproved by Reguera--Thiele.
We introduce an ultra-sensitive interferometric protocol that combines weak value amplification (WVA) with traditional interferometry. This protocol WVA + interferometry uses weak value amplification of the relative delay between two paths…
In this paper, we point out that the definition of weak tracial approximation can be improved and strengthened. An example of weak tracial approximation is also provided.
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to…
Nearly thirty years ago the possibility of anomalous weak amplfication (AWA) was revealed by Aharonov, Albert and Vaidman [1]. Recently two papers presents two AWA schemes which are beyond the traditional proposal given by them [14, 15]. At…
In this work it is shown that, in contrast to the strong and electromagnetic theories, additive conserved numbers (such as lepton, aromatic and another numbers) and gamma-5 anomaly do not appear in the standard weak interaction theory. It…
We discuss the (twisted) weak positivity theorem. We also treat some applications.
Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is…
Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state…
We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body Schroedinger operators, this leads to a limiting absorption principle that is uniform on the…
The technique of almost-balanced weak values amplification (ABWV) was recently proposed [Phys. Rev. Lett. 116: 100803 (2016)]. We demonstrate this technique using a modified Sagnac interferometer, where the counter-propagating beams are…
Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some…
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…
Encoding the imaginary part of a weak value onto an initially entangled probe can modify its entanglement content - provided the probe observable can distinguish between states of different entropies. Apart from fundamental interest, this…