The Studies On Quantum Steering And The Related Problems In The Open System

Quantum nonlocal correlations(abbreviated to QNC:quantum entanglement,quantum steering(Einstein-Podolsky-Rosen steering)and Bell nonlocality)play significant roles for displaying superiority in many quantum communication and computation tasks,and are also important resources to realize quantum information tasks.However,in a real quantum system,quantum system cannot avoid to interact with its surrounding external noise,which induces the rapid attenuation or even extinction of QNC,namely the so-called decoherence phenomena.Therefore,the study of dynamics behaviors of QNC in open systems and exploring to suppress the decoherence effect caused by the noise,and the intrinsic relations of among numerous quantum resources have far-reaching significance to promote people to better achieve quantum information tasks.In this dissertation,we investigate the dynamics of QNC in open systems,and how to effectively recover the lost Einstein-Podolsky-Rosen(EPR)steering in non-Markovian environments.We also study how the Unruh effect affects EPR steering and its redistribution under a non-inertial framework,and explore the intrinsic relations of among quantum resources within the composite system.The research results have been listed as follows:(1)We have investigated the dynamics behaviors of QNC when the single qubit of bipartite system interacts with the local noise channel.The results indicated that all entangled pure states and maximally entangled evolution states(EES)are steerable,and not every EES is steerable and some steerable states dissatisfy Bell nonlocality.Besides,EPR steering first experiences a "sudden death" and then immediately recovers with increasing decoherence strength in BF and PF channels.In PF and PD channels,all EES are steerable and obey Bell nonlocality when initially shared state is an entangled pure state.In BF channels,all steerable states have Bell nonlocality,but some EES cannot be employed to realize EPR steering.However,when initially shared state is an entangled mixed state,the outcomes are different from that of the entangled pure state.For another,the steerability of entangled mixed states is weaker than that of entangled pure states.(2)We have discussed the dynamics behaviors of EPR steering and how to effectively recover the lost steerability of quantum states within non-Markovian environments.We have considered two different cases:one-subsystem or total system interacts with the non-Markovian environments.It turns out that the non-Markovian environments can induce the quasi-periodic quantum entanglement resurgence,however,EPR steering cannot retrieve in the same condition,and the resurgent entanglement cannot be utilized to achieve EPR steering.Subsequently,based on the weak measurements,we have put forward a feasible physical scheme for recovering EPR steering in non-Markovian environments.The scheme consists of prior weak measurement on each subsystem before the interaction with non-Markovian environments followed by post reversal measurement.It is shown that the steerability of quantum states and the fidelity can be effectively restored.Furthermore,the larger the strength of weak measurement is,the better the effectiveness of the scheme to restore EPR steering is.(3)The dynamic behavior of EPR steering and its redistribution under a non-inertial framework have been investigated.Specifically,we have explored the scenario that particle A hold by Alice is in a flat space-time and another particle B by Bob entangled with A is in a Rindler space-time.The results showed that EPR steering from Alice to Bob is dramatically destroyed by Unruh effect caused by the acceleration of Bob.Besides,EPR steering has an asymmetry property,and EPR steering asymmetry increases with the growing intensity of Unruh effect.The redistribution of EPR steering showed that:the reduced physical accessible EPR steering from Alice to Bob is distributed to the physical inaccessible EPR steering(from Alice to anti-Bob or from Bob to anti-Bob).Notably,the redistribution of EPR steering is quite different from quantum entanglement and quantum discord,only one of EPR steering between from Alice to anti-Bob and from Bob to anti-Bob experiences a "sudden birth" with the increase of acceleration parameter,which means that they cannot simultaneously survive.That is,the monogamy relation of EPR steering is still tenable in such a scenario.Consequently,we believe that EPR steering could also be served as one of important resources in the long-distance quantum secure communication under the relativistic framework.(4)To reveal the intrinsic relations hidden in the quantum resources,we have investigated the intrinsic relations of bipartite quantum resources in the W-type states.The result showed that the interrelations among the degree of coherence,concurrence,Bell nonlocality and purity are presented.Considering Bell nonlocal and Bell local(satisfying the Bell-CHSH inequality)states for the two-qubit subsystems derived from the W-type states,we obtained lower and upper boundaries expressions of the degree of coherence versus concurrence.And also attained exact relation among the degree of coherence,concurrence and purity.Moreover,coherence is also closely related to entanglement in two specific scenarios:the W-type state under a noise channel and a renormalized spin-1/2 Heisenberg XXZ model.