On Several Problems Of Quantum Steering And Post-quantum Correlation

Quantum nonlocal correlation is one of the important differences between quantum world and classical world,and also is one of the most basic problems in quantum mechanics.Generally speaking,quantum nonlocal correlation can be divided into three forms:quantum entanglement,quantum steering and Bell nonlocality.At present,the research of quantum entanglement and Bell nonlocality is relatively mature,while the study of quantum steering has just started,there are still many problems to be solved.One of the fundamental problems is the verification of quantum steering.Although a lot of quantum steering criteria have been proposed,most of them provide sufficient conditions for verifying quantum steering.The calculation of some criteria need to run over all possible quantum states,and the computational complexity is extremely high.Some criteria are only applicable to the case of two-party low-dimensional quantum states and cannot be effectively extended to the case of multi-party high-dimensional states.In some criteria,state-dependent measurement operators or correlation weights need to be constructed.Undoubtedly,these issues limit the application range and feasibility of the existing quantum steering criteria greatly.So it is still a very challenging task to seek simple and effective quantum steering criteria.In addition,some properties of quantum steering,such as superactivation,need to be studied further.The superactivation of quantum steering is currently only known for isotropic states,and whether there exists examples other than isotropic states is so far an open question.Among all of the quantum nonlocal correlations,Bell nonlocal correlation is the strongest,which can be verified by the violation of Bell inequality.All classical correlations obey Bell inequality,while quantum nonlocal correlations can violate Bell inequality,and the maximum value of the violation is the Tsirelson limit(?).But quantum nonlocal correlations are not the strongest in principle.Some studies have shown that in the non-signaling theory,there exists such a correlation,whose nonlocality is stronger than that of quantum nonlocal correlation,which is beyond the Tsirelson limit and even reaches the maximum value 4.These correlations are referred to as post-quantum nonlocality,which can be simulated by non-signaling correlated box.Generally speaking,the stronger the nonlocal correlation is,the more powerful the information processing capacity it will possess.How to increase the nonlocality has attracted more and more attention.The existing protocols work well only for specific low-dimensional nonlocal correlation boxes,however,they cannot be generalized to higher-dimensional cases.The nonlocality distillation for higher-dimensional nonlocal correlation boxes needs further study.In view of the above problems,the current dissertation will focus on the following research topics:(1)Quantum steering criteria for bipartite quantum systemsStarting from the local hidden states model,we present a two-party two-dimensional nonlinear quantum steering criterion by using joint orthogonal measurements.The state-independent measurement operators or correlation weights makes this new criterion computable.Compared with the existing linear steering criterion or entropic criterion,ours can verify more steerable states.Based on the difference between the global and the local properties of quantum states,we present a representation-independent steering criterion for two-party arbitrary dimensional quantum systems,which works by comparing the purity of a bipartite quantum system with that of its subsystems.Compared with the local uncertainty relations criterion,our new criterion is readily computable,and can verify more steerable states than the existing linear steering criterion or entropic criterion.(2)Superactivation of quantum steeringQuantum resources can be superactivated,and the most typical examples of which are bound entanglement activation and Bell nonlocality activation.It has recently been discovered that quantum steering can be also superactivated,but this property is currently only known for isotropic states,and whether the steering for general quantum states can be superactivated is still unknown.Based on the complete local orthogonal measurement,we propose a scheme to activate the violation of local uncertainty relations(LUR)steering inequality for two-qubit X states.The result shows that two-qubit X quantum states can be activated.In addition,previous results indicate that the superactivation of low dimensional isotropic states requires a large number of copies.Although two copies are enough for the superactivation of steering,while the price is a high local dimension,and it is unclear whether superactivation is possible with few copies in low-dimensional systems such as two-qubit systems.By providing examples of activating LUR steering inequality with two copies in a two-qubit system,our work may open a potential way to this question.(3)Simulation and distillation of post-quantum correlationAs post-quantum correlation is a non-physical correlation,it cannot be realized directly in classical or quantum systems.However,it can be simulated by some methods,such as using Bell test loopholes or enlarging the Hilbert space.By using the fair-sampling loophole,we propose a scheme to simulate the post-quantum correlation in a two-party two-dimensional pre-selection and post-selection system,which can violate the Bell inequality to its maximum value 4.In addition,high-dimensional nonlocality distillation is much more complicated than low-dimensional cases.By designing the 'wirings' for the nonlocal correlation boxes,we propose a more universal nonlocality distillation scheme,which is more efficient and applicatable for both low-dimensional and high-dimensional quantum systems.