Related papers: Uncertainty Relations for Angular Momentum
We investigate the measurement uncertainties of a triple of positive operator-valued measures (POVMs) based on statistical distance, and formulate state-independent tight uncertainty inequalities satisfied by the three measurements in terms…
The uncertainty relation of three quantities in quantum mechanics is estimated in terms of commutators. The Pauli matrices are used to find a contribution of third-order commutators. The resulting inequality refines the Heisenberg…
The aim of the work is to give the explicit proofs of the Renyi-entropy uncertainty relations presented in the previous work [A. Rastegin, arXiv:0805.1777]. The relations with both the state-dependent and state-independent entropic bounds…
The uncertainty principle sets a bound on our ability to predict the measurement outcomes of two incompatible observables which are measured on a quantum particle simultaneously. In quantum information theory, the uncertainty principle can…
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
Uncertainty lower bounds for parameter estimations associated with a unitary family of mixed-state density matrices are obtained by embedding the space of density matrices in the Hilbert space of square-root density matrices. In the…
We show how preparation uncertainty relations that are formulated as sums of variances may be tightened by using the quantum Fisher information to quantify quantum fluctuations. We apply this to derive stronger angular momentum uncertainty…
Information-theoretic uncertainty relations formulate the joint immeasurability of two non-commuting observables in terms of information entropies. The trade-off of the accuracy in the outcome of two successive measurements manifests in…
Minimum uncertainty states of the conventional Heisenberg uncertainty relation have been extensively studied and are often regarded as the most classical quantum states from the perspective of uncertainty, providing valuable insight into…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
We propose an alternative measure of quantum uncertainty for pairs of arbitrary observables in the 2-dimensional case, in terms of collision entropies. We derive the optimal lower bound for this entropic uncertainty relation, which results…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
The uncertainty relation is a distinguishing feature of quantum theory, characterizing the incompatibility of noncommuting observables in the preparation of quantum states. Recently, many uncertainty relations were proposed with improved…
A geometric approach to formulate the uncertainty principle between quantum observables acting on an $N$-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a…
We investigate the product form uncertainty relations of variances for $n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations satisfied by three observables has been derived, which is shown to be better than the ones…
The Schr{\"o}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is…
The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the…
Uncertainty relations are a fundamental feature of quantum mechanics. How can these relations be found systematically? Here we develop a semidefinite programming hierarchy for additive uncertainty relations in the variances of non-commuting…
We discuss on the uncertainty relation (UR) for a closed one dimensional system (circle). In such a system, we cannot use the angle along the circle as a position variable. Otherwise we meet difficulties about the definition of the average…