Quantum uncertainty relations of quantum coherence and dynamics under amplitude damping channel

In this paper, we discuss quantum uncertainty relations of quantum coherence through a different method from Ref. [52]. Some lower bounds with parameters and their minimal bounds are obtained. Moreover, we find that for two pairs of measurement bases with the same maximum overlap, quantum uncertainty relations and lower bounds with parameters are different, but the minimal bounds are the same. In addition, we discuss the dynamics of quantum uncertainty relations of quantum coherence and their lower bounds under the amplitude damping channel（ADC）. We find that the ADC will change the uncertainty relations and their lower bounds, and their tendencies depend on the initial state.

Applying the Theory of Numerical Radius of Operators to Obtain Multi-observable Quantum Uncertainty Relations

Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables(i.e.,bounded or unbounded self-adjoint operators).By revealing a connection between standard deviations of quantum observables and numerical radius of operators,we establish a universal uncertainty relation for k observables,of which the formulation depends on the even or odd quality of k.This universal uncertainty relation is tight at least for the cases k=2 and k=3.For two observables,the uncertainty relation is a simpler reformulation of Schr?dinger’s uncertainty principle,which is also tighter than Heisenberg’s and Robertson’s uncertainty relations.

Quantum uncertainty relations of Tsallis relative α entropy coherence based on MUBs

In this paper,we discuss quantum uncertainty relations of Tsallis relative α entropy coherence for a single qubit system based on three mutually unbiased bases.For α∈[1/2,1)U(1,2],the upper and lower bounds of sums of coherence are obtained.However,the above results cannot be verified directly for any α∈(0,1/2).Hence,we only consider the special case of α=1/n+1,where n is a positive integer,and we obtain the upper and lower bounds.By comparing the upper and lower bounds,we find that the upper bound is equal to the lower bound for the special α=1/2,and the differences between the upper and the lower bounds will increase as α increases.Furthermore,we discuss the tendency of the sum of coherence,and find that it has the same tendency with respect to the different θ or φ,which is opposite to the uncertainty relations based on the Rényi entropy and Tsallis entropy.

Quantum uncertainty relations of two generalized quantum relative entropies of coherence

In this paper, we consider the quantum uncertainty relations of two generalized relative entropies of coherence based on two measurement bases. First, we give quantum uncertainty relations for pure states in a d-dimensional quantum system by making use of the majorization technique; these uncertainty relations are then generalized to mixed states. We find that the lower bounds are always nonnegative for pure states but may be negative for some mixed states. Second, the quantum uncertainty relations for single qubit states are obtained by the analytical method. We show that the lower bounds obtained by this technique are always positive for single qubit states. Third, the lower bounds obtained by the two methods described above are compared for single qubit states.

Controlling Entropic Uncertainty in the Presence of Quantum Memory by Non-Markovian Effects and Atom-Cavity Couplings

Based on the time-convolutionless master-equation approach, the entropic uncertainty in the presence of quantum memory is investigated for a two-atom system in two dissipative cavities. We find that the entropic uncertainty can be controlled by the non-Markovian effect and the atom-cavity coupling. The results show that increasing the atom-cavity coupling can enlarge the oscillating frequencies of the entropic uncertainty and can decrease the minimal value of the entropic uncertainty. Enhancing the non-Markovian effect can reduce the minimal value of the entropic uncertainty. In particular, if the atom-cavity coupling or the non-Markovian effect is very strong, the entropic uncertainty will be very dose to zero at certain time points, thus Bob can minimize his uncertainty about Alice＇s measurement outcomes,

Effect of weak measurement on quantum correlations

We investigate the local quantum uncertainty(LQU)in weak measurement.An expression of weak LQU is explicitly determined.Also,we consider some cases of three special X states,Werner state,circulant two-qubit states,and Heisenberg model via LQU in normal and weak measurements.We find that the LQU in weak measurement is weaker than the case of strong measurement.

Uncertainty relations based on skew information with quantum memory

Uncertainty principle is one of the most fascinating features of the quantum world. It asserts a fundamental limit on the precision with which certain pairs of physical properties of a particle, such as position and momentum, can not be si- multaneously known. The uncertainty principle has attracted considerable attention since the innovation of quantum me- chanics and has been investigated in terms of various types of uncertainty inequalities： in terms of the noise and dis- turbance, according to successive measurements, as informa- tional recourses in entropic terms, by means of majorization technique and based on sum of variances and standard devia- tions.

Nonclassical correlations in two-dimensional graphene lattices

We investigate nonclassical correlations via negativity,local quantum uncertainty(LQU)and local quantum Fisher information(LQFI)for two-dimensional graphene lattices.The explicitly analytical expressions for negativity,LQU and LQFI are given.The close forms of LQU and LQFI confirm the inequality between the quantum Fisher information and skew information,where the LQFI is always greater than or equal to the LQU,and both show very similar behavior with different amplitudes.Moreover,the effects of the different system parameters on the quantified quantum correlation are analyzed.The LQFI reveals more nonclassical correlations than LQU in a two-dimensional graphene lattice system.

Uncertainty Relations for Coherence

Quantum mechanical uncertainty relations are fundamental consequences of the incompatible nature of noncommuting observables.In terms of the coherence measure based on the Wigner-Yanase skew information,we establish several uncertainty relations for coherence with respect to von Neumann measurements,mutually unbiased bases(MUBs),and general symmetric informationally complete positive operator valued measurements(SIC-POVMs),respectively.Since coherence is intimately connected with quantum uncertainties,the obtained uncertainty relations are of intrinsically quantum nature,in contrast to the conventional uncertainty relations expressed in terms of variance,which are of hybrid nature(mixing both classical and quantum uncertainties).From a dual viewpoint,we also derive some uncertainty relations for coherence of quantum states with respect to a fixed measurement.In particular,it is shown that if the density operators representing the quantum states do not commute,then there is no measurement(reference basis)such that the coherence of these states can be simultaneously small.

Uncertainty relation of successive measurements based on Wigner-Yanase skew information

Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.

Entanglement,Identical Particles and the Uncertainty Principle

A new uncertainty relation(UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.