【作者】 邓峻峰；

【导师】 荆继良；

【作者基本信息】 湖南师范大学 ， 理论物理， 2011， 硕士

【摘要】 量子信息科学从诞生到现在虽只有10多年时间,但由于其重大的理论意义及广阔的应用前景而得以迅猛发展,扩展形成一片新兴的领域,并取得了引人瞩目的成就。量子纠缠是量子信息理论中的一个重要概念,它不但具有十分重要的理论意义,而且可以作为主要的资源应用于很多重要的量子信息操作中,如量子计算、量子通信等。广义相对论是物质世界的时空理论和时空中物质运动的普遍理论。黑洞物理是广义相对论理论中的一个重要部分,它联系了引力理论所描述的宏观世界和量子力学描述的微观世界。黑洞某些性质揭示了量子论和广义相对论之间的内在联系,在对量子信息理论的研究方面也具有十分重要的意义。近年来,在广义相对论框架下研究量子信息逐渐引起越来越多的人的兴趣,因为它不仅能进一步加深我们对量子信息的理解,而且还会在黑洞熵和黑洞信息疑难的研究中扮演重要的角色。作为广义相对论和量子信息的交叉学科,弯曲时空中量子信息已成为量子信息研究的新热点领域。我们将在广义相对论描述的弯曲时空中进行量子纠缠提纯的研究。本文讨论了史瓦西时空背景下狄拉克场的纠缠提纯问题。分析了霍金温度、场的能量对纠缠提纯的影响。研究发现对于初始的两粒子Werner态,在平直时空中,只有其态参数,F(0<F<1)取1/2<F<1时它才有纠缠。而当其中一个粒子盘旋在黑洞视界附近而处于弯曲时空中时,则只有在F取(?)<F<1((?)=3e(χ/Τ)+5/6e(ω/Τ)+8)的情况下,Werner态才有纠缠。初始态有纠缠的范围相对于平直时空发生了改变。我们发现,霍金温度Τ及场能量ω会影响到F取值下限(?)的大小。(?)随T的增加而增加,但随ω的增加而减少。当ω→0或Τ→∞时(?)→0.57。本文还探讨了当初始的Werner态由一般纠缠态组成时,其态参数α对纠缠提纯的影响。我们发现,参数α的取值对初始态的纠缠度大小有很明显的影响,并且在弯曲时空中会影响纠缠的衰减趋势,但在黑洞背景下,初始态有纠缠的范围并不受α的影响。更多还原

【Abstract】 Recently ten years, quantum information has developed very quickly because of it’s major theoretical significance and broad application prospect. Many emerg-ing fields have produced and a greatly achievement has been obtained. Quantum entanglement is both very important in the study of quantum infomation and is a major resource in quantum information, such as quantum teleportation and quan-tum computation and so on. On the other hand, general relativity is a theory about; spacetime and the movement of material. Black hole physics is an impor-tant part of the general relativity, which relates the theory of macroscopic world and microscopic world. So black hole physics have an important significance in the research of quantum imformation. Recently, more and more people are interested in reseach of the entanglement in a curved spaectime because it; is not only help us understand quantum information more clearly, but also very important in the black hole information paradox and the black hole entropy. Thus, considetable effort has been expended on the study of quantum entanglement in the curved spacetime. This thesis is devoted to the research of entanglement distillability in the black-hole spacetimeThe entanglement distillability for the Dirac field in the spacetime of the Schwarzschild black hole is investigated. For the prepared Werner state in the innertial frame, it is entangled for 1/2< F< 1. But in the spacetime of black hole, the state is entangled for T< F< 1 (where r=(?)). This is unlike the case of innertial frame. We found that the Hawking temperature T and the energyωof the state play an important role in the low boundary T. T increases with the rise of the temperature T but it reduces with the rise of theω. Whenω→0 or T→∞, we have T→0.57.We also investigate how the parameterαinfluences the entanglement dis-tillability when the prepared werner state is composed with uncertain entangled states. We found that although the parameterαaffects the entanglement, it does not change the range of the parameter F in which the state is entangled.更多还原