Quantum Information In Relativistic Framework

The integration of quantum mechanics, classical information theory, quan-tum field theory, relativity theory, as well as quantum optics, thermodynamics and statistics, gives birth to the theory of relativistic quantum information. Rel-ativistic quantum information aims at not only the effects of relativistic motions, relativistic effects, structure and nature of spacetime on the quantum resources, storage, manipulation and transmission of quantum information, but also the ap-plication of quantum technologies to detect the structure and nature of spacetime, and the interaction between gravity and matter, and so on. Without doubt, the research of quantum information in a relativistic setting will provide a more com-plete framework for the quantum information theory, and also will bring a lot of benefit to the detection of relativistic effects in noninertial and curved spacetime. This thesis is devoted to the investigation of bipartite and multipartite quantum entanglement, quantum correlation, quantum nonlocality, atomic geometric phase, atomic Lamb shift, quantum metrology in noninertial frames and curved space-time, as well as radiation spectra and information paradox of black hole. The main conclusions come as follows:First, we investigate how the motions of observers, and the nature of spacetime affect the classical and quantum decoherence, quantum entanglement and quan-tum nonlocaltiy of quantum systems. We find:(?) from the perspective of a non-inertial observer, the quantum correlation and measurement-induced nonlocality (MIN) for Dirac fields monotonously decrease as the acceleration of the observers increases, but the change of MIN for Bosonic fields is not monotonous. Besides, when the acceleration approaches the infinity limit, the MIN of the Bosonic fields vanishes, while that of the Dirac fields still exists. So, quantum resources and their evolution depend on the observers and statistic rules for different fields; (?) as the acceleration of detector increases, the bipartite entanglement between de-tectors will experience a "sudden death", while the tripartite entanglement will not, thus we argue that multipartite systems are better than bipartite systems to perform quantum information processing tasks in noninertial frames; (?) the thermal nature of de Sitter space and the motions of atoms will induce that the atomic entanglement decreases and suffers a "sudden death", so the structure and nature of space also affect quantum resources.Then, we treat the atom interacting with external fields as an open quantum system, and study its geometric phase, Lamb shift and quantum metrology. We find:(?) the geometric phase of both freely falling and static atoms in de Sitter spacetime obtain a thermal correction, the correction for the freely falling atom results from the Gibbons-Hawking effect, and that for the static atom comes from both the Gibbons-Hawking effect and Unruh effect. So, the correction to geometric phase of atom provides, in theory, us a different perspective to understand the thermal nature of de Sitter space; (?) the Lamb shift of the static atom in de Sitter is distance-dependent, and thus can create a Casimir-Polder like force on the atom, while the energy shift of the static atom in the thermal Minkowski space cannot, so this Casimir-Polder like force can be used to distinguish the de Sitter space from the thermal Minkowski space; (?)if the atom is considered as a detector to estimate Unruh temperature, the ultimate precision allowed by quantum mechanics can be obtained under two conditions, long enough time of the detector's evolution and the population measurement on the detector, so this precision for the estimation of Unruh temperature is within the capability of current technologies.Finally, we analyze the information paradox and six possible radiation spectra of Schwarzschild black hole. We find:(?) no matter for what kind of non-thermal radiation spectra, the total entropy taken away by all the radiation particles equals to the initial entropy of black hole, which means that during the evaporation of black hole, information is not lost, it is taken away by the radiations, and thus non-thermal spectra can provide a possibility to explain where the information of black hole goes; (?) for all of the thermal radiation spectra, the energy covariances of two successive emissions are exactly zero, while they are nontrivial for all the non-thermal spectra. Especially, there are distinctly different maximums of energy covariances for the temperature-corrected and energy-corrected non-thermal spec-tra. Consequently, these differences provide a possible way towards experimentally analyzing whether the radiation spectrum of black hole is thermal or non-thermal with or without high order quantum corrections.