Quantum Entanglement And Projective Measurement In Curved Spacetime

Quantum entanglement is both the central concept and the major resource in quantum information tasks such as quantum teleportation and quantum com-putation. Recently, it is widely accepted that understanding the entanglement in a relativistic framework is not only of interest to quantum information, but also plays an important role in black hole entropy and the black hole information paradox. Thus, much attention has been focused on the investigation of quantum entanglement in the relativistic framework. This thesis is devoted to the investi-gation of quantum entanglement and projective measurements in the black hole physics which is an intersectional field of general relativity, quantum mechanics, string theory, thermodynamics, statistics. Three interesting results are obtained:1) The entanglement of the coupled massive scalar field in the spacetime of a Garfinkle-Horowitz-Strominger(GHS) dilaton black hole is investigated. It is found that the entanglement does not depend on the mass of the particle and the coupling between the scalar field and the gravitational field, but it decreases as the dilaton parameter D increases. It is of interest to note that in the limit of D→M, corresponding to the case of an extreme black hole, the state has no longer distillable entanglement for any state parameter a, but the mutual infor-mation equals to a nonvanishing minimum value, which indicates that the total correlations consist of classical correlations plus bound entanglement in this limit.2) The entanglement of the Dirac field in the asymptotically flat black hole is studied. Unlike the bosonic case in which the initial entanglement vanishes in the limit of infinite Hawking temperature, in this case the entanglement achieves a nonvanishing minimum values, which shows that the entanglement is never com-pletely destroyed when black hole evaporates completely. Another interesting re-sult is that the mutual information in this limit equals to just half of its own initial value, which may be an universal property for any fields.3) The effects of projective measurements on the generation of entangled particles between two Dirac modes are investigated. It is shown that the pro-jective measurements made by Bob who locates near the event horizon of the Schwarzschild black hole will create entangled particles detected by Alice who stays stationary at the asymptotically flat region. It is found that the degree of entanglement decreases as the frequency of the detected particles increases and approaches to zero as the frequencyωk→∞, but the degree of entanglement increases as the Hawking temperature increases. Especially, the particle state is unentangled when the Hawking temperature is zero and approaches a maximally entangled Bell state when the black hole evaporates completely.