Related papers: Optimal Quantum Estimation for Gravitation

In the history of quantum mechanics, various types of uncertainty relationships have been introduced to accommodate different operational meanings of Heisenberg uncertainty principle. We derive an optimized entropic uncertainty relation…

We present a table-top quantum estimation protocol to measure the gravitational acceleration $g$ by using an optomechanical cavity. In particular, we exploit the non-linear quantum light-matter interaction between an optical field and a…

Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…

A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…

Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is an extensive debate over the question how the sensitivity scales with the resources (such as the average photon number) and…

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…

One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…

Consider a statistical model with an epistemic restriction such that, unlike in classical mechanics, the allowed distribution of positions is fundamentally restricted by the form of an underlying momentum field. Assume an agent (observer)…

In this essay, we argue that certain aspects of the measurement require revision in Quantum Gravity. Using entropic arguments, we propose that the number of measurement outcomes and the accuracy (or the range) of the measurement are limited…

Thermometry is a fundamental parameter estimation problem which is crucial in the development process of natural sciences. One way to solve this problem is to the extensive used local thermometry theory, which makes use of the classical and…

Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…

In recent years several ideas for experimental searches of effects induced by quantum properties of space-time have been discussed. Some of these ideas concern the role in quantum spacetime of the ordinary Lorentz symmetry of classical flat…

In the study of quantum limits to parameter estimation, the high dimensionality of the density operator and that of the unknown parameters have long been two of the most difficult challenges. Here we propose a theory of quantum…

It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the…

We consider two variants of a quantum-statistical generalization of the Cramer-Rao inequality that establishes an invariant lower bound on the mean square error of a generalized quantum measurement. The proposed complex variant of this…

Uncertainty relations are usually formulated as trade-off relations between two or more observables. Here we show that the uncertainty of a single observable already has a nontrivial lower bound originating from the noncommutativity between…

The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…

A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…

We critically discuss the measure of very short time intervals. By means of a "gedankenexperiment", we describe an ideal clock based on the occurrence of completely random events. We show that the minimum time interval Delta t that this…

This paper is a generalization of earlier papers [Nucl. Phys. B 884, 344 (2014) (arXiv:1312.2759) and JHEP 6, 63 (2015) (arXiv:1401.2488)]. We generalize the idea of quantum clock time to quantum spacetime reference frame via physical…