Related papers: On uncertainty relations in noncommutative quantum…
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 review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was…
Uncertainty relations express limits on the extent to which the outcomes of distinct measurements on a single state can be made jointly predictable. The existence of nontrivial uncertainty relations in quantum theory is generally considered…
Our knowledge of quantum mechanics can satisfactorily describe simple, microscopic systems, but is yet to explain the macroscopic everyday phenomena we observe. Here we aim to shed some light on the quantum-to-classical transition as seen…
The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
Uncertainty relations play a central role in quantum mechanics. Entropic uncertainty relations in particular have gained significant importance within quantum information, providing the foundation for the security of many quantum…
This paper presents the uncertainty related to position and momentum localization of a quantum state in terms of entropic uncertainty relations. We slightly improve the inequality given in [Phys. Rev. A 74, 052101 (2006)] and introduce a…
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…
Uncertainty relation lies at the heart of quantum mechanics, characterizing the incompatibility of non-commuting observables in the preparation of quantum states. An important question is how to improve the lower bound of uncertainty…
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $\Delta A$ and $\Delta B$ calculated…
The uncertainty relation is a distinctive characteristic of quantum theory. The uncertainty is essentially rooted in quantum states. In this work we regard the uncertainty as an intrinsic property of quantum state and characterize it…
Uncertainty principle is one of the cornerstones of quantum theory. In the literature, there are two types of uncertainty relations, the operator form concerning the variances of physical observables and the entropy form related to entropic…
Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
Majorization uncertainty relations are generalized for an arbitrary mixed quantum state $\rho$ of a finite size $N$. In particular, a lower bound for the sum of two entropies characterizing probability distributions corresponding to…