Exploring The Quantum-memory-assisted Entropic Uncertainty Relation In Open Systems

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 on 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 uncertainty relation continue thorough research,the inequation has been improved continually.Our research focuses on the dynamics of entropy uncertainty relation during the noise and the two-qubit Heisenberg XX model with inhomogeneous magnetic field,and proposes filtering operation on the particle to be measured under the channels.The main results have been listed as following:(1)In this work,we have investigated the dynamic features of the entropic uncertainty for two incompatible measurements under local unital and non-unital channels.Herein,we choose Pauli operators ?x and ?z as a pair of observables of interest measuring on particle A,the uncertainty can be predicted when particle A is entangled with quantum memory B.We explore the dynamics of the uncertainty for the measurement under local unitary(phase-damping)and nonunitary(amplitude-damping)channels,respectively.Remarkably,we also investigate the entropic uncertainty relation under three different kinds of measurements of Pauli-observable pair under a noisy environment;it has been found that the entropic uncertainty has the same tendency of its evolution during the AD and PD channel when we choose ?x and ?y measurement.Notably,we find out that the entropic uncertainty will have an optimal value if one chooses ?x and ?z as the measurement incompatibility.Furthermore,in order to reduce the entropic uncertainty in noisy environment,we propose an effective strategy to reduce the amount by means of implementing a filtering operation on the particle under these two types of channels,respectively.It turns out that this operation can greatly reduce the entropic uncertainty by modulation of the operation strength.Thus,our investigations might offer an insight into the dynamics and steering of the entropic uncertainty in an open system.(2)In this work,we investigate the quantum-memory-assisted entropic uncertainty relation in a two-qubit Heisenberg XX model with inhomogeneous magnetic field.It has been found that larger coupling strength J between the two spin-chain qubits can effectively reduce the entropic uncertainty.Besides,we observe the mechanics of how the inhomogeneous field influences the uncertainty,and find out that when the inhomogeneous field parameter b<1,the uncertainty will decrease with the decrease of the inhomogeneous field parameter b,conversely,the uncertainty will increase with decreasing b under the condition that b>1.Intriguingly,the entropic uncertainty can shrink to zero when the coupling coefficients are relatively large,while the entropic uncertainty only reduces to 1 with the increase of the homogeneous magnetic field.Additionally,we observe the purity of the state and Bell non-locality,and obtain that the entropic uncertainty is anti-correlated with both the purity and Bell non-locality of the evolution state.