Related papers: Generalized uncertainty relations
We derive the lower bound of uncertainty relations of two unitary operators for a class of states based on the geometric-arithmetic inequality and Cauchy-Schwarz inequality. Furthermore, we propose a set of uncertainty relations for three…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Schroedinger-Robertson (SR) uncertainty…
Historically, the element of uncertainty in quantum mechanics has been expressed through mathematical identities called uncertainty relations, a great many of which continue to be discovered. These relations use diverse measures to quantify…
Generalized uncertainty relations may depend not only on the commutator relation of two observables considered, but also on mutual correlations, in particular, on entanglement. The equivalence between the uncertainty relation and Bohr's…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
We derive generalised uncertainty relations (GURs) for angular momentum and spin in the smeared-space model of quantum geometry. The model implements a minimum length and a minimum linear momentum, and recovers both the generalised…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
Constructive techniques to establish state-independent uncertainty relations for the sum of variances of arbitrary two observables are presented. We investigate the range of simultaneously attainable pairs of variances, which can be applied…
We show that the uncertainty relation as expressed in the Robertson-Schrodinger generalized form can be used to detect the mixedness of three-level quantum systems in terms of measureable expectation values of suitably chosen observables…
In quantum mechanics, the variance-based Heisenberg-type uncertainty relations are a series of mathematical inequalities posing the fundamental limits on the achievable accuracy of the state preparations. In contrast, we construct and…
In this paper we provide a new set of uncertainty principles for unitary operators using a sequence of inequalities with the help of the geometric-arithmetic mean inequality. As these inequalities are "fine-grained" compared with the…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
Entropic uncertainty relation (EUR) formulates the restriction of the inherent uncertainty of quantum mechanics from the information-theoretic perspective. A tighter lower bound for uncertainty relations can provide information-theoretic…
Uncertainty relations express the fundamental incompatibility of certain observables in quantum mechanics. Far from just being puzzling constraints on our ability to know the state of a quantum system, uncertainty relations are at the heart…
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized…
We derive a thermodynamic uncertainty relation for general open quantum dynamics, described by a joint unitary evolution on a composite system comprising a system and an environment. By measuring the environmental state after the…
We outline a new model in which generalised uncertainty relations are obtained without modified commutation relations. While existing models introduce modified phase space volumes for the canonical degrees of freedom, we introduce new…
The generalized uncertainty principle (GUP) is a modification of standard quantum mechanics due to Planck scale effects. The GUP has recently been used to improve the short distance behaviour of classical black hole spacetimes by invoking…
We study universally valid uncertainty relations in general quantum systems described by general $\sigma$-finite von Neumann algebras to foster developing quantitative analysis in quantum systems with infinite degrees of freedom such as…
Recently, Maccone and Pati have given two stronger uncertainty relations based on the sum of variances and one of them is nontrivial when the quantum state is not an eigenstate of the sum of the observables. We derive a family of weighted…