本文選題：黑洞 + 量子信息　； 參考：《湖南師范大學》2011年碩士論文

【摘要】：量子信息科學從誕生到現(xiàn)在雖只有10多年時間,但由于其重大的理論意義及廣闊的應用前景而得以迅猛發(fā)展,擴展形成一片新興的領域,并取得了引人矚目的成就。量子糾纏是量子信息理論中的一個重要概念,它不但具有十分重要的理論意義,而且可以作為主要的資源應用于很多重要的量子信息操作中,如量子計算、量子通信等。廣義相對論是物質世界的時空理論和時空中物質運動的普遍理論。黑洞物理是廣義相對論理論中的一個重要部分,它聯(lián)系了引力理論所描述的宏觀世界和量子力學描述的微觀世界。黑洞某些性質揭示了量子論和廣義相對論之間的內(nèi)在聯(lián)系,在對量子信息理論的研究方面也具有十分重要的意義。近年來,在廣義相對論框架下研究量子信息逐漸引起越來越多的人的興趣,因為它不僅能進一步加深我們對量子信息的理解,而且還會在黑洞熵和黑洞信息疑難的研究中扮演重要的角色。作為廣義相對論和量子信息的交叉學科,彎曲時空中量子信息已成為量子信息研究的新熱點領域。我們將在廣義相對論描述的彎曲時空中進行量子糾纏提純的研究。 本文討論了史瓦西時空背景下狄拉克場的糾纏提純問題。分析了霍金溫度、場的能量對糾纏提純的影響。研究發(fā)現(xiàn)對于初始的兩粒子Werner態(tài),在平直時空中,只有其態(tài)參數(shù),F(0F1)取1/2F1時它才有糾纏。而當其中一個粒子盤旋在黑洞視界附近而處于彎曲時空中時,則只有在F取(?)F1((?)=3e(χ/Τ)+5/6e(ω/Τ)+8)的情況下,Werner態(tài)才有糾纏。初始態(tài)有糾纏的范圍相對于平直時空發(fā)生了改變。我們發(fā)現(xiàn),霍金溫度Τ及場能量ω會影響到F取值下限(?)的大小。(?)隨T的增加而增加,但隨ω的增加而減少。當ω→0或Τ→∞時(?)→0.57。 本文還探討了當初始的Werner態(tài)由一般糾纏態(tài)組成時,其態(tài)參數(shù)α對糾纏提純的影響。我們發(fā)現(xiàn),參數(shù)α的取值對初始態(tài)的糾纏度大小有很明顯的影響,并且在彎曲時空中會影響糾纏的衰減趨勢,但在黑洞背景下,初始態(tài)有糾纏的范圍并不受α的影響。
[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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