The Study Of Monogamy Relations Of Different Quantum Correlations Under Typical Noisy Channels

Quantum correlation is one of the essential characteristics of Quantum Mechanics,and is also an imperative resource in the quantum information processing.Quantum correlation includes not only quantum entanglement,but also quantum discord,Bell nonlocality and EPR steering.The distribution of quantum correlation has the property of monogamy,which means that quantum correlation cannot be shared freely in multi-partite systems.In 2017,Shuming Cheng et al.studied the anisotropic invariance of 3-qubit,and the monogamy relations between this invariance and different quantum correlations(Phys.Rev.Lett.118,010401,2017).However,the effect of the noise needs to be considered in the actual quantum information processing,and the effect of noise channels on the anisotropic invariance and distribution of quantum correlations needs futher consideration.In this thesis,we mainly research the monogamy distributions of different quantum correlations under local bit-flipped channel,and further,we have proved that the isotropic and anisotropic invariances of 3-qubit pseudo-pure state under global depolarizing channel,and studied the impacts of channels on the distribution of Bell correlation.The thesis contains three chapters.In the first chapter,we introduce the measurements of quantum correlations in the multi-partite system,which includes Bell nonlocality,EPR steering,3-tangle,quantum discord and the fidelity of remote state preparation,isotropic and anisotropic invariances of 3-qubit and so on.In the second chapter,we mainly study the effect of local bit-flipped channel on the monogamy distributions of different quantum correlations of pure 3-qubit systems.Here,the pure 3-qubit system we use involves a pure 2-qubit state and a single qubit of environment as a control bit to make one of that 2-qubit get bit-flipped;accordingly,we get a local bit-flipped channel.We study the effects of the bit-flipped probability and the amplitude of the pure 2-qubit state on the monogamy of Bell correlation,Bell correlation and the distribution character of quantum entanglement,Bell correlation and the anisotropic,quantum discord and the fidelity of remote state preparation among subsystems.Surprisingly,we find the distribution of Bell correlation among AB's and AC's subsystems in pure 3-qubit state will be saturated,and not rely on the bit-flipped probability and the amplitude of the pure 2-qubit state.In the third chapter,we prove the isotropic and anisotropic invariances of 3-qubit pseudo-pure state,which is under global depolarization channel.And we find that the isotropic invariance is equal to the depolarizing probability squared,and the presentation of anisotropic invariance is as same as the presentation of pure 3-qubit state.Further,we analyze how both depolarizing channel and bit-flipped channel effcect on Bell correlations and their distributions among the subsystems in the three-partite systems.