Theoretical Study On Steering Phenomena In Quantum Systems

Quantum steering is a fundamental feature of a compound quantum system,describing the ability of one subsystem in the compound quantum system to affect other ones by virtue of local measurements.It has been considered one of the most well-known nonlocal phenomena in quantum mechanics,which lies in between quantum entanglement and Bell nonlocality according to the hierarchy of nonlocal correlation.Unlike quantum entanglement and Bell nonlocality,quantum steering exhibits some asymmetric properties,due to which quantum steering has found important applications in one-way quantum information processing and become one distinguishable research field in quantum information science.Nowadays,a widely concerned research topic in quantum steering is to establish the relations between quantum steering and other quantum resources and find new applications of quantum steering in quantum information science.The present thesis aims to systematically address this topic and the main findings are summarized as follows:First,we have investigated the relations between quantum steering and the first-order coherence,for which we have established the complementary relations between the maximum violation of three-setting linear steering inequality and the first-order coherence and proved that the maximum violation of the three-setting linear steering inequality can quantify the hidden coherence.As is well-known,quantum coherence and quantum nonlocality are two fundamental features of quantum mechanics and both of them are important quantum resources in quantum information processing.While the relations of the first-order coherence to Bell nonlocality and to entanglement have been established,an interesting open question is how to quantitatively characterize the relation of the first-order coherence to steering,which is one kind of nonlocal correlations lying in between Bell nonlocality and entanglement.We have found that the first-order coherence for each subsystem in a compound system has a complementary relation with the maximum violation of the three-setting linear steering inequality.A weighted sum of their squares keeps invariant under unitary operations,although both of them change their values in general.This suggests that the maximum violation of the three-setting linear steering inequality can be taken as a measure of hidden coherence.The proposed complementary relation has been verified experimentally in optical systems.Second,we have investigated the relations between quantum steering ellipsoid and quantum phase transitions,for which we have proposed a geometrically visible method to detect quantum phase transitions.We have demonstrated the feasibility of this method by taking the XXZ model as an example and found that the quantum steering ellipsoid associated with the XXZ model changes in shape with the quantum phase transitions occurred in the model;that is,it is a needle in the ferromagnetic phase,an oblate spheroid in the gapless phase,and a prolate spheroid in the antiferromagnetic phase.The transition from the needleshaped ellipsoid to the oblate ellipsoid corresponds to the first order quantum phase transition,and the transition from the oblate ellipsoid to the prolate ellipsoid corresponds to the Kosterlitz-Thouless phase transition.Compared with other methods based on quantum correlation measures such as entanglement,quantum discord,and Bell nonlocality,the proposed method can capture not only the strength of quantum correlation but also the types of quantum correlation.Moreover,compared with other geometric methods for detecting phase transitions with fidelity and Berry phase,the proposed method has the merit of being geometrically visible.Third,we have proposed a new coherence measure,dubbed the steeringinduced coherence,and further shown how to exploit it to detect quantum phase transitions.Taking the XXZ model and the Kitaev honeycomb model as two examples,we have demonstrated that the steering-induced coherence can detect not only the first-order phase transition of the XXZ model but also the KosterlitzThouless phase transition of the XXZ model and the topological phase transition of the Kitaev honeycomb model.So far,many methods based on coherence measures have been proposed to detect quantum phase transitions.However,it is known that the coherence measures adopted in the previous works are basisdependent,and choosing a different basis generally alters their values,which may put the role of these coherence measures as detectors of quantum phase transitions into question.By contrast,the steering-induced coherence is basis-independent and,moreover,it can detect the Kosterlitz-Thouless phase transition in XXZ model,which cannot otherwise be detected by the known coherence measures examined so far.