Related papers: Uncertainty relations for any multi observables
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…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
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…
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…
We conjecture new uncertainty relations which restrict correlations between results of measurements performed by two separated parties on a shared quantum state. The first uncertainty relation bounds the sum of two mutual informations when…
We study a possible improvement of uncertainty relations. The Heisenberg uncertainty relation employs commutator of a pair of conjugate observables to set the limit of quantum measurement of the observables. The Schroedinger uncertainty…
We consider particles prepared by the von Neumann-L\"uders projection. For those particles the standard deviation of the momentum is discussed. We show that infinite standard deviations are not exceptions but rather typical. A necessary and…
Generalized uncertainty principles are able to serve as useful descriptions of some of the phenomenology of quantum gravity effects, providing an intuitive grasp on non-trivial space-time structures such as a fundamental discreteness of…
Uncertainty relations state that there exist certain incompatible measurements, to which the outcomes cannot be simultaneously predicted. While the exact incompatibility of quantum measurements dictated by such uncertainty relations can be…
We present a new uncertainty relation by defining a measure of uncertainty based on skew information. For bipartite systems, we establish uncertainty relations with the existence of a quantum memory. A general relation between quantum…
Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible…
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…
For a pair of observables, they are called "incompatible", if and only if the commutator between them does not vanish, which represents one of the key features in quantum mechanics. The question is, how can we characterize the…
Uncertainty relations and quantum entanglement are pivotal concepts in quantum theory. Beyond their fundamental significance in shaping our understanding of the quantum world, they also underpin crucial applications in quantum information…
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…
In its original formulation, Heisenberg's uncertainty principle describes a trade-off relation between the error of a quantum measurement and the thereby induced disturbance on the measured object. However, this relation is not valid in…
We derive an uncertainty relation for two unitary operators which obey a commutation relation of the form UV=exp[i phi] VU. Its most important application is to constrain how much a quantum state can be localised simultaneously in two…
Uncertainty principle is the basis of quantum mechanics. It reflects the basic law of the movement of microscopic particles. Wigner-Yanase skew information, as a measure of quantum uncertainties, is used to characterize the intrinsic…
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…