Related papers: Weighted Uncertainty Relations
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should use when doing any calculation using the entangled wave function of the pair. This new…
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…
The canonical Robertson-Schr\"{o}dinger uncertainty relation provides a loose bound for the product of variances of two non-commuting observables. Recently, several tight forward and reverse uncertainty relations have been proved which go…
We present the entropic uncertainty relations for multiple measurement settings in quantum mechanics. Those uncertainty relations are obtained for both cases with and without the presence of quantum memory. They take concise forms which can…
For a simple set of observables we can express, in terms of transition probabilities alone, the Heisenberg Uncertainty Relations, so that they are proven to be not only necessary, but sufficient too, in order for the given observables to…
Minimum-uncertainty squeezed states, related to a broad class of observables, are analyzed. Methods for characterizing such states are developed, which are based on numerical solutions of ordinary differential equations. As typical examples…
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…
Sharp uncertainty relations restricting the values of variances in the position space and in the momentum (wavevector) space are derived. They have the same form $\Delta r\Delta k\ge 5/2$ in the classical theory of light beams, in the…
We report on experimental studies on entanglement quantification and verification based on uncertainty relations for systems consisting of two qubits. The new proposed measure is shown to be invariant under local unitary transformations, by…
We study uncertainty relations for pairs of conjugate variables like number and angle, of which one takes integer values and the other takes values on the unit circle. The translation symmetry of the problem in either variable implies that…
The uncertainty principle sets limit on our ability to predict the values of two incompatible observables measured on a quantum particle simultaneously. This principle can be stated in various forms. In quantum information theory, it is…
Quantum states can be subjected to classical measurements, whose incompatibility, or uncertainty, can be quantified by a comparison of certain entropies. There is a long history of such entropy inequalities between position and momentum.…
The uncertainty principle and entanglement are two fundamental, but yet not well understood, features of quantum theory. The uncertainty relation reflects the capability limit in acquiring the knowledge of different physical properties of a…
We describe a setup for obtaining uncertainty relations for arbitrary pairs of observables related by Fourier transform. The physical examples discussed here are standard position and momentum, number and angle, finite qudit systems, and…
A scheme for construction of uncertainty relations (UR) for n observables and m states is presented. Several lowest order UR are displayed and briefly discussed. For two states |\psi> and |\phi> and canonical observables the (entangled)…
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 ask which is the best strategy to reveal uncertainty relations between comple- mentary observables of a continuous variable system for coarse-grained measurements. This leads to the derivation of new uncertainty relations for…