Related papers: Complementarity and the uncertainty relations
The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation…
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…
The example of nonpositive trace-class Hermitian operator for which Robertson-Schroedinger uncertainty relation is fulfilled is presented. The partial scaling criterion of separability of multimode continuous variable system is discussed in…
We investigate uncertainty relations for quantum observables evolving under non-Hermitian Hamiltonians, with particular emphasis on the role of metric operators. By constructing appropriate metrics in each dynamical regime, namely the…
In [Berta 2014 Entanglement], uncertainty relations in the presence of quantum memory was formulated for mutually unbiased bases using conditional collision entropy. In this paper, we generalize their results to the mutually unbiased…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Uncertainty relations involving complementary observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum…
The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other…
Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator…
The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…
Establishing the correspondence of two dimensional paraxial and three dimensional non-paraxial optical beams with the qubit and qutrit systems respectively, we derive a complementary relation between Hilbert-Schmidt coherence, generalized…
Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal…
We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the…
We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…
The Ehrenfest theorem and the Robertson uncertainty relation are well-known basic equations in quantum mechanics. However, there exist problematic cases, where the Ehrenfest theorem and the Robertson uncertainty relation are not correct.…
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…
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…
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…
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…