Related papers: Relation between fundamental estimation limit and …
The quantum multiparameter estimation is very different from the classical multiparameter estimation due to Heisenberg's uncertainty principle in quantum mechanics. When the optimal measurements for different parameters are incompatible,…
In this work we determine a lower bound to the mean value of the quantum potential for an arbitrary state. Furthermore, we derive a generalized uncertainty relation that is stronger than the Robertson-Schr\"odinger inequality and hence also…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
Heisenberg uncertainty principle describes a basic restriction on observer's ability of precisely predicting the measurement for a pair of non-commuting observables, and virtually is at the core of quantum mechanics. We herein aim to study…
In this note, we consider the implications of the Heisenberg uncertainty principle (HUP) when computing uncertainties that affect the main dynamical quantities, from the perspective of special relativity. Using the well-known formula for…
The uncertainty principle lies at the heart of quantum mechanics, as it describes the fundamental trade-off between the precision of position and momentum measurements. In this work, we study the quantum particle in the Boltzmann states and…
In quantum sensing and metrology, an important class of measurement is the continuous linear measurement, in which the detector is coupled to the system of interest linearly and continuously in time. One key aspect involved is the quantum…
The Heisenberg inequality \Delta X \Delta P \geq \hbar/2 can be replaced by an exact equality, for suitably chosen measures of position and momentum uncertainty, which is valid for all wavefunctions. The statistics of complementary…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
We propose that whatever quantity controls the Heisenberg uncertainty relations (for a given complementary pair of observables) it should be identified with an effective Planck parameter. With this definition it is not difficult to find…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
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 study the quantum-mechanical uncertainty relation originating from the successive measurement of two observables $\hat{A}$ and $\hat{B}$, with eigenvalues $a_n$ and $b_m$, respectively, performed on the same system. We use an extension…
The Heisenberg uncertainty principle states that the product of the noise in a position measurement and the momentum disturbance caused by that measurement should be no less than the limit set by Planck's constant, hbar/2, as demonstrated…
In quantum mechanics, measurements cause wavefunction collapse that yields precise outcomes, for non-commuting observables such as position and momentum Heisenberg's uncertainty principle limits the intrinsic precision of a state. Although…
Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…
In recent years, novel quantifications of measurement error in quantum mechanics have for the first time enabled precise formulations of Heisenberg's famous but often challenged measurement uncertainty relation. These relations take the…
Unlike well-established parameter estimation, function estimation faces conceptual and mathematical difficulties despite its enormous potential utility. We establish the fundamental error bounds on function estimation in quantum metrology…