Study On Dynamics Of Entanglement-assisted Entropic Uncertainty

In recent years,the entropic uncertainty relation has been widely applied in the region of quantum information science.More recently,Berta et al.have derived the quantum-memory-assisted entropic uncertainty,which brings much influence on later researches.Now,this conceptual relation is of fundamental importance in quantum cryptography,detecting entangled states,and construction of error-correcting codes for communicating quantum or private classical information.In addition,with the advance of the quantum information science,the inequation has been greatly improved.Our research focuses on the dynamics of entropy uncertainty relation during the noisy channel and the two-qutrit Heisenberg spin-1 model with inhomogeneous magnetic field,and we propose PT-symmetric operation on the particle to be measured under the channels.The main results have been listed as follows:(1)In this work,we attempt to observe entropic uncertainty in the presence of quantum memory under different local noisy channels.To be specific,we develop the dynamics of the measured uncertainty under local phase-bit-flipping(unital)and depolarization(nonunital)noise,respectively,and attractively put forward an effective strategy to manipulate its magnitude of the uncertainty of interest by means of parity-time symmetric(PT-symmetric)operations on the subsystem to be measured.It is interesting to find that there exist different evolution characteristics of the uncertainty in the channels considered here,i.e.,the monotonic behavior in the nonunital channels,and the non-monotonic behavior in the unital channels.Moreover,the amount of the measured uncertainty can be reduced to some degree by properly modulating the PT-symmetric operations(2)We examine the quantum-memory-assisted entropic uncertainty relations(QMA-EUR)in two-qutrit spin-1 Heisenberg XYZ and XXX chains under homogeneous magnetic fields,respectively.We specifically derive the dynamical evolution of QMA-EUR for various incompatible measurements on Pauli operators(mutually unbiased bases)and SU(3)generators in the Heisenberg XXX and XYZ models when spin A is the object to be measured and B is served as quantum memory during information processing.Notably,it has been found in the case of mutual unbiased-base measurements that,firstly,the larger coupling strength J between A and B can induce the degradation of the measurement's uncertainty;secondly,the entropic uncertainty is extremely dependent on the coupling strength and the external magnetic field,which would bring the uncertainty on the inflation.In addition,we unveil the dynamical behaviors of the uncertainty measured on SU(3)generators,and it proves that the uncertainty's dynamics are subtly different from those in the former Moreover,we explore the relationship between the entropic uncertainty and the system's entanglement(negativity)and declare that the dynamics of the entropic uncertainty of interest are approximately anti-correlated with that of negativity.At last,the entanglement's dynamics of the probed system in the XXX and XYZ models are revealed and analyzed by means of negativity,respectively.Hence,our observations might pave the way to understand the dynamical traits of the entropic uncertainty during measurement-based information processing.