Related papers: Uncertainty Relations for Angular Momentum
We consider the Heisenberg uncertainty principle of position and momentum in 3-dimensional spaces of constant curvature $K$. The uncertainty of position is defined coordinate independent by the geodesic radius of spherical domains in which…
Four expressions involving sums of position and velocity coordinates bounding the total angular momentum of particle systems, and by extension of any continuous or discontinuous material systems, are derived which are tighter for any…
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 optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
Uncertainty relations are usually stated as bounds on selected combinations of variances, but the full covariance matrix contains substantially richer information about the geometry of quantum state space and about the operational…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
Measurement uncertainty relations are quantitative bounds on the errors in an approximate joint measurement of two observables. They can be seen as a generalization of the error/disturbance tradeoff first discussed heuristically by…
How much unavoidable randomness is generated by a Positive Operator Valued Measure (POVM)? We address this question using two complementary approaches. First we study the variance of a real variable associated to the POVM outcomes. In this…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in…
The angular uncertainty principle (angular-UP) states the orbital angular momentum (OAM) is precisely defined in an optical vortex with angular position (AP) ranging over 2{\pi} azimuthal coordinate ({\phi}). However, the pair of observable…
We consider successive measurements of position and momentum of a single particle. Let P be the conditional probability to measure the momentum k with precision dk, given a previously successful position measurement q with precision dq.…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We define an uncertainty observable, acting on several replicas of a continuous-variable bosonic state, whose trivial uncertainty lower bound induces nontrivial phase-space uncertainty relations for a single copy of the state. By exploiting…
In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
We point out that the Gaussian wave-packet formalism can serve as a concrete realization of the joint measurement of position and momentum, which is an essential element in understanding Heisenberg's original philosophy of the uncertainty…