Quantum Nonlocality And Joint Measurability

The main topic of quantum computation and quantum information is to process information processing tasks by using quantum mechanical systems.The quantum cor-relations are the most important resource of quantum computation and quantum infor-mation processing.The mathematical description and quantification of correlations in quantum systems has attracted a lot of attention in recent years.In view of quantum entanglement,quantum states are divided into parts:separable states and entangled s-tates.From the view of correlations,there exist states of local correlations and states of nonlocal correlations.It is interesting that some separable states may be of non-classical correlations(discord)and some entangled states do not exhibit non-locality.This thesis contains six parts.The first part is about basic knowledge of quantum computation and quantum information.The last part is the summary.The main work of my Ph.D.thesis is showed in the chapters from two to five.In the second chapter,we study the concurrence of arbitrary dimensional bipartite quantum systems.By using a set of positive but not completely positive maps,we present an analytical lower bound of concurrence.This lower bound can be used as entanglement detection.It can also improve some existing lower bounds.In the third chapter,we investigate two problems.We first investigate the non-locality distributions among the reduced pairwise qubit systems of multi-qubit systems.This non-locality is based on the maximal violations of the CHSH inequality of the reduced pairwise qubit systems.We present a trade-off relation satisfied by these maximal violations,which gives rise to restrictions on the distribution of non-locality among the sub-qubit systems.For a three-qubit system,it is impossible that all pairs of qubits violate the CHSH inequality.And once a pair of qubits violates the CHSH inequality maximally,the other two pairs of qubits must both obey the CHSH inequality.It is generalized to arbitrary multi-qubit systems.We then consider the maximal violation of the CHSH inequality and Vertesi inequality about quantum states under local filter operations.The local hidden variable models admitting by these quantum states are presented.And then we find that they can give rise to Bell violation after applying suitable local filters.This clarifies the genuine hidden non-locality:some LHV entangled states may show non-locality after local filtering.In the fourth chapter we investigate the product form uncertainty relations of vari-ances for n(n?3)quantum observables.In particular,tight uncertainty relations satis-fied by three observables are derived,which is shown to be better than the ones derived from the strengthened Heisenberg and the generalized Schrodinger uncertainty relations,and some existing uncertainty relation for three spin-half operators.Uncertainty rela-tion of arbitrary number of observables is also derived.As an example,the uncertainty relation satisfied by the eight Gell-Mann matrices is presented.In the fifth chapter we investigate the triple-wise joint measurability of three unbiased observables of a qubit.The sufficient and necessary condition of jointly measurability for three unbiased observables is derived.This condition can give rise to a measure of the degree of incompatibility of three given sharp observables of a qubit.According to[Phys.Rev.Lett.111,160405(2013);Phys.Rev.A 89,012129(2014)],we generalize the combined approximation errors of three sharp observables and derived the bound from the measure of the incompatibility,which gives rise to a new quantum uncertainty relation that can be experimentally verified.