Entanglement Of Quantum States In Inertial And Noninertial Frames

The non-classical property of quantum states is one of the most important resources in quantum information processing, such as quantum entanglement teleportation, quantum key distribution and quantum computations. The proposal of quantum information processing was initially put forward in quantum systems, which was based on the discrete variables, and then the proposal based on continuous variable was also paid much attention. Besides, it plays a significant role in quantum optics, quantum communications, and information theory in the field of condensed matter theory. For continuous variable quantum systems, the Gaussian quantum states have been one of the main objects of study. However, in order to realize the quantum information and quantum computing tasks better, it is expected to prepare the quantum states with high degree of entanglement, high fidelity of teleportation, and strong ability to resist decoherence. And this is one of the important topics in the field of quantum information, which makes a turn to the non-Gaussian entangled states. In addition, the properties of quantum states have been studied deeply in non-inertial frames. Thus, the dissertation studied the non-classical property of non-Gaussian entangled states in inertial frame, and the entanglement of multi-body quantum states.The main contents are:In the inertial frame, the dissertation introduced the properties of non-Gaussian quantum state with continuous variables. Firstly, the paper proposed a kind of non-Gaussian entangled state which was an Hermite polynomial excited squeezed vacuum by extending the wave-packet states with a vortex structure to a general case.Its normalization factor is just related to the Legendre polynomial, a concise form. By using the coordinate state and two-mode entangled state representations as well as the IWOP technique, the paper has derived the state vector corresponding to the general vortex state. It is shown that the vortex state can be reformed to the Hermite polynomial excited squeezed vacuum in two kinds of representations. In particular,the paper has given the condition that the general case reduces to the special case mentioned above for the vortex state in coordinate state representation. Then the paper investigated the statistical properties according to the photon number distribution and the Wigner function(WF) in phase space. As an application of the vortex state, the paper considered the quantum teleportation of the coherent state. It is shown that the parameters in the generalized state can be used to modulate the photon-number distribution, the negative region and vortex structure of the WF, and the teleportation fidelity of the coherent state. Noting that the photon-subtraction can be used to generate the state with a vortex structure, thus it would be interesting to consider if we can achieve the vortex state by the superposition of photon-subtraction operators. The paper will further consider this problem and make some comparisons about theentanglement and the teleportation with the vortex state obtained by photon-addition operators in the future.In the non-inertial frame, the paper considered the properties of entanglement for four Fermi particles. For simplicity, the paper only examined the ideal case without the effect of noise. It is shown that:(i) a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated;(ii)for one to three acceleration cases, both the whole entanglement and the one among some parts decrease as the increasing parameter r, and the corresponding values of entanglement decrease as the increasing number of accelerated observers. In the limit of infinite acceleration case, i.e., r →π/4, there is still entanglement for all tangles;(iii) only when are there four acceleration observers, the phenomena of entanglement sudden death will be present not only for the whole entanglement but also for the part one. For instance, when the parameter r exceeds about 0.417, the whole entanglement will be zero. In addition, the degree paper made a comparison between two definitions of entanglement. It is shown that the value of differences increase as the parameter r for one accelerated observer. However, it is interesting to notice that, for both two and three accelerated observer, the absolute value of differences increase and then decrease as the increasing parameter r. And there will be the maximum when r ?0.6798 and r ?0.512.