Related papers: Breaking the weak Heisenberg limit

Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a…

We give a visually appealing counterexample to the proposition that unbiased estimators are better than biased estimators.

We show that ultraviolet information can be extracted from low-energy expansion coefficients, assuming analyticity and the absence of massless singularities. By reorganizing the low-energy expansion through an inverse Laplace transform and…

We prove an inequality on positive real numbers, that looks like a reverse to the well-known Hilbert inequality, and we use some unusual techniques from Fourier analysis to prove that this inequality is optimal.

We prove the Hasse principle and weak approximation for varieties defined over number fields by the nonsingular intersection of pairs of quadratic forms in 8 variables. The argument develops work of Colliot-Thelene, Sansuc and…

We provide a lower bound on the probability that a binomial random variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial random variables.

Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…

An upper bound between the information gain and state reversibility of weak measurement was first developed by Y. K. Cheong and S. W. Lee [Phys. Rev. Lett. 109, 150402 (2012)]. Their results are valid for arbitrary d-level quantum systems.…

This paper focuses on parameter estimation and introduces a new method for lower bounding the Bayesian risk. The method allows for the use of virtually \emph{any} information measure, including R\'enyi's $\alpha$, $\varphi$-Divergences, and…

We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…

We propose an optical read-out scheme allowing a demonstration of principle of information extraction below the diffraction limit. This technique, which could lead to improvement in data read-out density onto optical discs, is independent…

Motivated by LHC results, we modify the usual criterion for naturalness by ignoring the uncomputable power divergences. The Standard Model satisfies the modified criterion ('finite naturalness') for the measured values of its parameters.…

For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…

We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…

Using a quantum version of the Bell-Ziv-Zakai bound, I derive a Heisenberg limit to multiparameter estimation for any Gaussian prior probability density. The mean-square error lower bound is shown to have a universal quadratic scaling with…

This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of…

We show explicitly, for different types of extremal black holes, that test fields satisfying the null energy condition at the event horizon cannot violate the weak cosmic censorship conjecture. This is done by checking, in each case, that…

Parameter estimates for associated genetic variants, report ed in the initial discovery samples, are often grossly inflated compared to the values observed in the follow-up replication samples. This type of bias is a consequence of the…

We build upon recent work on using Machine Learning models to estimate Hamiltonian parameters using continuous weak measurement of qubits as input. We consider two settings for the training of our model: (1) supervised learning where the…