Spin Squeezing And Entropic Uncertainty Relation Under Bosonic Reservoirs

Entanglement,a special quantum correlation,has been applied widely in many fields.So far,although the few-body entanglement has been very clear for us,a good measure of multi-body mixedness entangled states is still absent.It was believed by many studies that the multi-body entanglement can be witnessed by spin squeezing to some extent.Moreover,spin squeezing is useful in the fields of high precision measurement and quantum information and so on.Nowadays,the research of spin squeezing is still one of the interested issues in the world.The uncertainty principle is an important rule of quantum theory,which restricts our ability to simultaneously predict the measurement outcomes of two incompatible observables.It is described by a variety of relations,which are known as uncertainty relations.In recent years,the entropic uncertainty relations has attracted much interest due to the potential applications in entanglement witness and quantum key distribution,etc.As is well known,the interaction between quantum system and surrounding environment may lead to the appearance of quantum decoherence.It will be harmful to the realization of quantum information processing.In order to utilize quantum resources better,it is very significant to study the dynamical behaviors of quantum systems in open systems.This thesisdiscussesthedynamicsofspinsqueezingandthe quantum-memory-assisted entropic uncertainty relation based on the multi-qubit system coupled to multiple bosonic reservoirs.The main results are as follows:1.The effects of the non-Markovian properties,reservoirs'number and quantum weak measurement on the spin squeezing and entanglement are discussed.It is shown that the dynamics of spin squeezing and entanglement is non-Markovian when the reservoirs'number ₁N is increased in the weak coupling regime,while we find that spin squeezing and entanglement present the oscillating behaviors with time.But,in contrast to the Markovian regime,the existence of environmental memory effect is not beneficial to the keep of spin squeezing and entanglement.Nevertheless,in the strong coupling regime the stronger non-Markovian effect can improve the spin squeezing and entanglement in some time periods.In additions,for the stronger non-Markovianity spin squeezing and entanglement can obtain their minimal values in a shorter initial time and display more oscillations with larger amplitudes.Finally,the manipulation of quantum weak measurements on spin squeezing and entanglement is explored and the relative ideal results are got.2.The influences of the non-Markovian properties,reservoirs'number and local filtering operation on the quantum-memory-assisted entropic uncertainty relation and mixedness are analyzed.It is found that uncertainty isn't always correlated with mixedness,and with the increasing of reservoirs'number or non-Markovianity:?1?uncertainty and mixedness can acquire their maximal values in a shorter initial time and become a stable value at last after a number of oscillations;?2?uncertainty and mixedness can be lowered to some degree;?3?the filtering operation is a very effective scheme to reduce uncertainty and mixedness.