黑洞时空中的量子纠缠提纯

发布时间：2018-05-22 20:27

  本文选题：黑洞 + 量子信息　； 参考：《湖南师范大学》2011年硕士论文

【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(0F1)取1/2F1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(?)F1((?)=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。
[Abstract]:Quantum information science has been developed rapidly because of its great theoretical significance and broad application prospects, and it has been expanded into a new field, and has made remarkable achievements, although it has only been born to the present for more than 10 years. Quantum entanglement is an important concept in quantum information theory. It not only has very important theoretical significance, but also can be used as a main resource in many important quantum information operations, such as quantum computation, quantum communication, etc. General relativity is the space-time theory of matter world and the universal theory of material motion in space-time. Black hole physics is an important part of the theory of general relativity. It links the macroscopic world described by the gravitational theory and the micro-world described by quantum mechanics. Some properties of black hole reveal the internal relationship between quantum theory and general relativity, and it is also of great significance in the study of quantum information theory. In recent years, the study of quantum information in the framework of general relativity has gradually attracted more and more people's interest, because it can not only further deepen our understanding of quantum information. It also plays an important role in the study of black hole entropy and black hole information. As an interdisciplinary subject of general relativity and quantum information, quantum information in curved space-time has become a new hot field of quantum information research. We will study the purification of quantum entanglement in the curved spacetime described by general relativity. In this paper, we discuss the entanglement purification of Dirac field under the background of Schwarzie space-time. The effects of Hawking temperature and field energy on entanglement purification are analyzed. It is found that for the initial two-particle Werner state, it is entangled only when the state parameter F _ (F _ (0) F _ (1) is taken from the 1/2F1 in a flat spacetime. When one of the particles hovers near the event horizon of the black hole and is in a curved spacetime, the Werner state is entangled only if F is taken from the black hole and the F _ (1) is 3 e( 蠂 / T) 5 / 6e (蠅 / T) 8). The range of entanglement in the initial state has changed relative to the flat spacetime. We find that Hawking temperature T and field energy 蠅 affect the lower limit of F value. ) It increases with the increase of T, but decreases with the increase of 蠅. When omega 0 or T 鈭，

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