Related papers: Breaking the weak Heisenberg limit
Let $k$ be an integer which is the difference between prime numbers infinitely often. It is known that there are infinitely many such $k$ and, in this paper, we give a new unconditional proof that these $k$ have positive density and improve…
Current metrological bounds typically assume full control over all particles that are involved in the protocol. Relaxing this assumption we study metrological performance when only limited control is available. As an example, we measure a…
In this paper, we shall study the existence of weak solutions to Hessian type equations on compact Riemannian manifolds without boundary.
A sharper uncertainty inequality which exhibits a lower bound larger than that in the classical N-dimensional Heisenberg's uncertainty principle is obtained, and extended from N-dimensional Fourier transform domain to two N-dimensional…
Weak supervision enables efficient development of training sets by reducing the need for ground truth labels. However, the techniques that make weak supervision attractive -- such as integrating any source of signal to estimate unknown…
Present data, both from direct Higgs search and from analysis of electroweak data, are starting to become rather restrictive on the possible values for the mass of the standard model Higgs. We discuss a new physics scenario based on a model…
We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.
We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…
This paper resolves two open problems from a recent paper, arXiv:2403.16981, concerning the sample complexity of distributed simple binary hypothesis testing under information constraints. The first open problem asks whether interaction…
In this short note we explain how one can use established results to prove various versions of the positive mass theorem for initial data sets with boundary, in dimensions less than 8.
Using the classical argument about tree level unitarity breakdown in combination with the precision electroweak data, it is shown, that if part of the Higgs sector is heavy and strongly interacting, this part is small and is out of range of…
We study the outcomes in a general measurement with postselection, and derive upper bounds for the pointer readings in weak measurement. Using the idea of weak measurement, we study Hardy's gedanken experiment and show how the "negative…
We address the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements, and modular variables, We present a physical explanation for the…
The Heisenberg limit is acknowledged as the ultimate precision limit in quantum metrology, traditionally implying that root mean square errors of parameter estimation decrease linearly with the time T of evolution and the number N of…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…
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…
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
We generalise a result of Heath-Brown and Skorobogatov to show that a certain class of varieties over a number field $k$ satisfies Weak Approximation and the Hasse Principle, provided there is no Brauer-Manin obstruction.
In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…