Quantum Nonlocality Of Continuous-variable Entangled States

Quantum nonlocality is one of the amazing properties in quantum theory. Although, quantum theory (from nonrelative quantum mechanics to relative quantum field theories) describes the world in terms of locality, like the classic theory. But as far as its essence concerned, quantum theory is still a space nonlocal theory in terms of locality. The nonlocal property has been displayed. There are more and more experiments to test the nonlocality. Studying the quantum nonlocality is of great importance to the basic problems in quantum theorems and quantum information theory.This thesis is composed of six chapter. The first chapter is aimed to introduce the history and some main fruits of quantum nonlocality.The second part introduces the basic theories of quantum nonlocality including EPR paradox and the completeness of quantum mechanics, the Bell inequality and its violation and the generalized CHSH inequality and its maximal violation. Then emphasis of this part is to introduce the Bell-type theorem with inequalties.The third chapter investigates the quantum nonlocaity of entangled coherent states, which is an important continuous-variable entangled states and can be generated in experiment. This part introduces two general methods to calculate the quantum nonlocality of entangled coherent states. Then we propose a new method to make the Bell-CHSH inequality reach the maximal violation value 2(2^1/2). This method has the probability to realize in experiment. Then we find the Bell operator which can make the entangled coherent states get the optimal quantum nonlocality theoretically.The fourth chapter studies the quantum nonlocality of the k-photon subtraction squeezed vacuum states, which is another continuous-variable entangled states and can be generated in experiments. It is a non-Gaussian quantum state and can be used to test the nonlocality experimently. This chapter emphasizes on the Bell-CHSH inequality of the two-mode k-photon subtractionvacuum states in terms of pseudospin operators. We find that the subtraction of photons can enhance the quantum nonlocality of these states. Then we further study the effect the decoherence has on the Bell-CHSH inequality.The fifth chapter introduces the Bell-type quantum nolocal theorem without inequalities. This chapter make a genenralization of GHZ, Hardy and Ca-bello theorem without inequality. Then we propose a new continuous-variable Cabello theorem, which used super-entangled states with parity and polarization freedoms and give a method without inequality to test quantum nonlocality. This is an All-Versus-Nothing method.The second section of the third chapter, the second and the third sections of the fourth chapter and the second section of the fifth chapter are inivations.In the sixth chapter we give a concise conclusion of this thesis and make an expectation of the future in this field.