The Theoretical And Experimental Investigations Concerning Quantum Steering And Relevant Problems

Quantum nonlocality is one of the important characteristics of quantum world different from classical world,which plays an essential role in the argument of Einstein-Podolsky-Rosen(EPR)paradox concerning the incompleteness of quantum mechanics.After then,Schr(?)dinger noted an essential point that one party can instantaneously influence the wave function of the distant another party by performing local measurement.He considered this phenomenon as quantum steering and also investigated its characteristics.However,based on the redefinition of quantum steering by Wiseman et al.in recent years,quantum steering has attracted significant interest in the field of quantum information science,and a series of achievements have obtained in both theory and experiment.In the modern view,quantum steering represents the case that the conditional state of one party cannot be described by using a local hidden state model.Hence,quantum steering is regarded as a quantum nonlocality between quantum entanglement and Bell nonlocality.It has many advantages and potential application values in the fields of quantum key distribution,subchannel discrimination,quantum communication,randomness generation,and so on.On the description of quantum states,any one-qubit state can be visually represented by employing a corresponding vector in the Bloch sphere.In the framework of quantum steering ellipsoid constructed by Jevtic et al.,quantum steering ellipsoid is used to faithfully describe any two-qubit state.On the one hand,this work provides an intuitive tool and a new avenue for characterizing any two-qubit state.On the other hand,it is also benefit to explore and establish a diagnostic tool of quantum nonlocality independent of reference system.Subsequently,the sufficient and necessary conditions for whether a quantum steering ellipsoid corresponding to a two-qubit state were obtained by Milne et al.,which deepen our cognition and understanding concerning quantum steering ellipsoid.Recently,many efforts were devoted to visually exploring the characteristics of two-qubit states via quantum steering ellipsoid,including quantum entanglement,quantum discord,quantum steering,and so on.Thereby,the visual investigations of various quantum resources through quantum steering ellipsoid have gradually become a new and hot topic in the field of quantum information,and it also opens a new road for exploring different quantum resources.These efforts embody important values in understanding these quantum resources from the perspective of geometry.The contents of this thesis mainly concentrate on the investigations of quantum steering and quantum steering ellipsoid.Theoretically,the maximal steered coherence and concurrence of two-qubit system are examined under the framework of quantum steering ellipsoid.Experimentally,using linear optical system,we investigate the quantum steering criterion based on a general entropic uncertainty relation,and realize the observation of quantum steering for two-qubit state by employing the scenario of entanglement detection.In addition,the complementarity relations between quantum steering criteria are demonstrated in experiment.Some achievements have been made both in theory and experiment,mainly theoretical and experimental results are as follows.1.Theoretical explorations of maximal steered coherence and quantum entanglement through quantum steering ellipsoid frameworkPractically,a quantum system can unavoidably interact with environmental noise,and the quantum resources degenerate in an irreversible way.Therefore,how to establish and investigate the relationships between quantum resources and quantum steering ellipsoid in noisy environment and visually explore quantum resources are important and new research contents in the field of quantum information.In this chapter,we derive the quantum steering ellipsoid of two-qubit Werner state suffering from a reservoir,and establish the dependence of the maximal steered coherence and concurrence on the geometric parameters of quantum steering ellipsoid.The influences of the strong coupling regime and weak coupling regime on the maximal steered coherence and concurrence are investigated in the framework of quantum steering ellipsoid.The results reveal that the maximal steered coherence can be visually characterized via the x or y semiaxis length of quantum steering ellipsoid,and the concurrence depends on the x and z semiaxes lengths of quantum steering ellipsoid.In the non-Markovian environment,the ellipsoid can shrink,inflate and move in the Bloch sphere due to that the information can flow bidirectionally between the quantum system and environment.On the contrary,in the Markovian environment,the quantum steering ellipsoid gradually degrades and ultimately vanishes at the north pole of Bloch sphere since the information gradually degenerates.As a consequence,the aforementioned characteristics of quantum steering ellipsoid can visually map the effects of the strong coupling regime and weak coupling regime on the maximal steered coherence and concurrence.Of particular note,it is found that the suppression of ellipsoidal semiaxis' s degradation can enhance maximal steered coherence and concurrence of system.In view of this,we realize the inflation of quantum steering ellipsoid by using filtering operation.Based on quantum steering ellipsoid,we derive the condition for increasing maximal steered coherence,and obtain the optimal operation strength of filtering operation.No matter in strong coupling regime or weak coupling regime,one can use the optimal operation strength to freeze the maximal steered coherence and concurrence.Our work provides a new avenue for investigating quantum resources and its protection in noise environment,and expands the application of quantum steering ellipsoid in quantum information.2.Experimental investigations of the steering criterion based on a general entropic uncertainty relationThe detection of quantum steering can be realized by violating various quantum steering criteria(namely,quantum steering inequalities).Among of them,steering criteria from entropic uncertainty relations are simple in concept,the criteria have been widely explored,and it can also expose the relations between quantum steering and entropic uncertainty relations.Previous efforts mostly depended on Shannon entropy.Presently,replacing the Shannon entropy with Tsallis entropy,Costa et al.attained the steering criterion based on a general entropic uncertainty relation(SCG).In order to test the ability of detecting quantum steering of the SCG in experiment,we prepare two-photon Werner-like states,realize Pauli measurements,and experimentally investigate the SCG in the linear optics experimental system.The results show that one can conveniently and effectively capture the quantum steering of two-photon quantum states via the SCG in experiment.Beyond this,our experimental results indicate that the SCG is superior to the linear quantum steering criterion in detecting the steerability of Werner-like states.It is worthwhile to note that our experimental process of examining SCG does not need to carry out the quantum state tomography.It effectively simplifies the complexity of experimental techniques for capturing quantum steering and reduces the consumptions of quantum resources in the experiment.3.Experimental realize the observations of quantum steering via entanglement detectionIn the past few years,the quantum steering have demonstrated in plenty of experimental efforts.Nevertheless,these efforts mostly need to choose the corresponding steering criterion and measurement setting.Generally speaking,the entanglement of a quantum state can be demonstrated by witnessing the quantum steering of the state(that is,if the quantum state exists quantum steering,then the state must exist entanglement).However,the converse is not always true.In principle,the observation of the quantum steering is more difficult than the observation of entanglement.In this chapter,without using any quantum steering criterion and measurement setting,we experimentally achieve the observations of quantum steering for two-qubit states by detecting entanglement.To be specific,based on each prepared two-qubit state(called “target state”)in linear optical experiment system,we successfully construct two new states,and detect the quantum steering of target state by capturing the entanglement of these new states.The results demonstrate that the entanglement of newly constructed state provide a new way for witnessing the steerability of two-qubit state.For this reason,our experimental results verify that one can transform the detection of quantum steering into the detection of quantum entanglement in experiment.Comparing with the scenario of two projective measurement setting,the scenario of entanglement detection in this chapter can observe the quantum steering of two-qubit states more effectively.4.Experimentally examining complementarity relations between quantum steering criteriaQuantum coherence and quantum steering are deemed as two essential and important quantum resources in the field of quantum information.The establishment of the connection between them is conducive to deeply understand their role in quantum information.Moreover,the construction of complementary relation between different physical quantities is one of significant open problems in the field of quantum information.Here,based on prepared two-photon Bell-like states and Pauli measurements,we experimentally investigate coherence steering criteria and confirm the existence of the complementarity relations between these criteria.The results verify that all prepared two-photon Bell-like states cannot violate three measurement setting inequalities in different coherence measures,and the inequalities establish a set of complementarity relations between two measurement setting coherence steering criteria and one measurement setting coherence steering criteria.Under the constraints of the complementary relations,if prepared Bell-like states violate two measurement setting coherence steering criteria and are steerable states,these states must obey one measurement setting coherence steering criteria as a compensation.Besides,our experimental results also certify that the observation of steerability for two-qubit state can be realized through the detection of subsystem's quantum coherence in experiment.In the efficiency of detecting the quantum steering of Bell-like states,two measurement setting coherence steering criterion based on skew information of coherence is strongest and can observe more steerable Bell-like states.Our work demonstrates the relation between quantum steering and quantum coherence,and also provides a new method to detect quantum steering of two-qubit system,viz.,two-qubit system's quantum steering can be witnessed by capturing the subsystem's quantum coherence.