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量子纠缠与宇宙学弗里德曼方程

王灿灿

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量子纠缠与宇宙学弗里德曼方程

王灿灿

Quantum entanglement and cosmological Friedmann equations

Wang Can-Can
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  • 量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球(a geodesic ball)的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.
    Quantum entanglement the most important part of quantum information theory, represents the intrinsic property of quantum states. It is a magical physical phenomenon in the form of nonlocality in the multi quantum system. The entanglement entropy as a measure of quantum information, has become an important tool, which provides a new research method for various subjects in physics. The study of the notion of quantum entanglement can provide a tool for understanding the cosmological features. In this work, we consider the cosmological applications of the entanglement in order to understand the cosmological dynamics from the entanglement point of view. The relation between the quantum information theory and the cosmology is studied. Employing Fermi normal coordinates (FNC) and conformal Fermi coordinates, we establish a relation between Friedmann equations of Friedmann-Lemaitre-Robertson-Walker universe and entanglement. Assuming that the entanglement entropy in a geodesic ball is maximized in a fixed volume and the entanglement is the basic element of the spacetime, we derive Friedmann equations from the first law of entanglement. Friedmann equations are first derived in the Fermi normal coordinate system, where the diamond size l is much smaller than the local curvature length, but still much larger than Planck scale lp. If the diamond size is comparable to the UV scale lUV, the quantum gravity effect becomes strong. Then we extend the discussion about the area deficit of the geodesic ball so that a freely falling observer can report observations and local experiments. In the cosmological context, the FNC are only valid on a scale much smaller than the Hubble horizon. Then we relax the small ball limitation by introducing conformal Fermi coordinates (CFCs). In the CFC system, we mainly focus on the flat universe with vanishing curvature of the space k=0. The Friedmann equations are derived in the CFC system. From the first law of entanglement the emergence of gravity can be described by the change in entanglement SA caused by matter HA angle. In this paper, we study the cosmology in a new framework with the viewpoint that spacetime geometry is viewed as an entanglement structure of the microscopic quantum state, and derive the Friedmann equations for the universe from the first law of entanglement We also briefly review the first law of entanglement. The study shows that there is a basic relation between the gravitation and quantum entanglement, which is valid for the solution of the gravitational field equation.
      通信作者: 王灿灿, can199217@shu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11375110)资助的课题.
      Corresponding author: Wang Can-Can, can199217@shu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11375110).
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    Rangamani M, Takayanagi T 2017 Lect. Notes Phys. 93 1

    [2]

    van Raamsdonk M 2010 Gen. Rel. Grav. 42 2323

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    Ryu S, Takayanagi T 2006 Phys. Rev. Lett. 96 181602

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    Nishioka T, Ryu S, Takayanagi T 2009 J. Phys. A 42 504008

    [6]

    Lashkari N, McDermott M B, van Raamsdonk M 2014 JHEP 1404 195

    [7]

    Jacobson T 2016 Phys. Rev. Lett. 116 201101

    [8]

    Manasse F K, Misner C W 1963 J. Math. Phys. 4 735

    [9]

    Dai L, Pajer E, Schmidt F 2015 JCAP 2015 43

    [10]

    Blanco D D, Casini H, Hung L Y, Myers R C 2013 JHEP 8 060

    [11]

    Takahashi Y, Umezawa H 1996 Int. J. Mod. Phys. B 10 1755

    [12]

    Cai R G, Kim S P 2005 JHEP 2 50

    [13]

    Unruh W G 1976 Phys. Rev. D 14 870

    [14]

    Cai R G, Cao L M 2007 Phys. Rev. D 75 064008

    [15]

    Ge X H 2007 Phys. Lett. B 651 49

    [16]

    Bueno P, Min V S, Speranza A J, Visser M R 2017 Phys. Rev. D 95 046003

    [17]

    Ge X H, Matsuo Y, Shu F W, Sin S J, Tsukioka T 2008 JHEP 810 9

    [18]

    Ge X H, Sin S J 2009 JHEP 905 51

    [19]

    Ge X H, Sin S J, Wu S F, Yang G H 2009 Phys. Rev. D 80 104019

    [20]

    Cai R G 2008 Prog. Theor. Phys. Suppl. 172 100

    [21]

    Gong Y, Wang A 2007 Phys. Rev. Lett. 99 211301

    [22]

    Cai R G, Cao L M, Hu Y P 2009 Classical and Quantum Gravity 26 155018

    [23]

    Cai R G, Ohta N 2010 Phys. Rev. D 81 1014

    [24]

    Cai R G, Cao L M, Hu Y P, Kim S P 2008 Phys. Rev. D 78 124012

    [25]

    Cai R G, Cao L M, Hu Y P 2008 JHEP 0808 090

    [26]

    Cai R G, Cao L M, Ohta N 2010 Phys. Rev. D 81 084012

    [27]

    Cai R G, Cao L M, Hu Y P, Ohta N 2009 Phys. Rev. D 80 104016

    [28]

    Zhu T, Ren J R 2009 Eur. Phys. J. C 62 413

    [29]

    Bamba K, Geng C Q 2009 Phys. Lett. B 679 282

    [30]

    Zhu T, Ren J R, Li M F 2009 Phys. Lett. B 674 204

    [31]

    Eisert J, Cramer M, Plenio M B 2010 Rev. Mod. Phys. 82 277

    [32]

    Ryu S, Takayanagi T 2006 Phys. Rev. Lett. 96 181602

  • [1]

    Rangamani M, Takayanagi T 2017 Lect. Notes Phys. 93 1

    [2]

    van Raamsdonk M 2010 Gen. Rel. Grav. 42 2323

    [3]

    Ge X H, Wang B 2018 JCAP 2018 047

    [4]

    Ryu S, Takayanagi T 2006 Phys. Rev. Lett. 96 181602

    [5]

    Nishioka T, Ryu S, Takayanagi T 2009 J. Phys. A 42 504008

    [6]

    Lashkari N, McDermott M B, van Raamsdonk M 2014 JHEP 1404 195

    [7]

    Jacobson T 2016 Phys. Rev. Lett. 116 201101

    [8]

    Manasse F K, Misner C W 1963 J. Math. Phys. 4 735

    [9]

    Dai L, Pajer E, Schmidt F 2015 JCAP 2015 43

    [10]

    Blanco D D, Casini H, Hung L Y, Myers R C 2013 JHEP 8 060

    [11]

    Takahashi Y, Umezawa H 1996 Int. J. Mod. Phys. B 10 1755

    [12]

    Cai R G, Kim S P 2005 JHEP 2 50

    [13]

    Unruh W G 1976 Phys. Rev. D 14 870

    [14]

    Cai R G, Cao L M 2007 Phys. Rev. D 75 064008

    [15]

    Ge X H 2007 Phys. Lett. B 651 49

    [16]

    Bueno P, Min V S, Speranza A J, Visser M R 2017 Phys. Rev. D 95 046003

    [17]

    Ge X H, Matsuo Y, Shu F W, Sin S J, Tsukioka T 2008 JHEP 810 9

    [18]

    Ge X H, Sin S J 2009 JHEP 905 51

    [19]

    Ge X H, Sin S J, Wu S F, Yang G H 2009 Phys. Rev. D 80 104019

    [20]

    Cai R G 2008 Prog. Theor. Phys. Suppl. 172 100

    [21]

    Gong Y, Wang A 2007 Phys. Rev. Lett. 99 211301

    [22]

    Cai R G, Cao L M, Hu Y P 2009 Classical and Quantum Gravity 26 155018

    [23]

    Cai R G, Ohta N 2010 Phys. Rev. D 81 1014

    [24]

    Cai R G, Cao L M, Hu Y P, Kim S P 2008 Phys. Rev. D 78 124012

    [25]

    Cai R G, Cao L M, Hu Y P 2008 JHEP 0808 090

    [26]

    Cai R G, Cao L M, Ohta N 2010 Phys. Rev. D 81 084012

    [27]

    Cai R G, Cao L M, Hu Y P, Ohta N 2009 Phys. Rev. D 80 104016

    [28]

    Zhu T, Ren J R 2009 Eur. Phys. J. C 62 413

    [29]

    Bamba K, Geng C Q 2009 Phys. Lett. B 679 282

    [30]

    Zhu T, Ren J R, Li M F 2009 Phys. Lett. B 674 204

    [31]

    Eisert J, Cramer M, Plenio M B 2010 Rev. Mod. Phys. 82 277

    [32]

    Ryu S, Takayanagi T 2006 Phys. Rev. Lett. 96 181602

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出版历程
  • 收稿日期:  2018-04-25
  • 修回日期:  2018-05-28
  • 刊出日期:  2018-09-05

量子纠缠与宇宙学弗里德曼方程

    基金项目: 国家自然科学基金(批准号:11375110)资助的课题.

摘要: 量子纠缠作为量子信息理论中最核心的部分,代表量子态一种内在的特性,是微观物质的一种根本的性质,它是以非定域的形式存在于多子量子系统中的一种神奇的物理现象.熵也是量子信息理论的重要概念之一,纠缠熵作为量子信息的一个测度已经成为一种重要的理论工具,为物理学中的各类课题提供了新的研究方法.本文主要考虑量子纠缠的宇宙学应用,试图更好地从纠缠的角度来理解宇宙动力学.本文研究了量子信息理论的概念和宇宙学之间的深层联系,利用费米正则坐标和共形费米坐标构建了弗里德曼- 勒梅特-罗伯逊-沃尔克宇宙学弗里德曼方程和纠缠之间的联系.假设小测地球(a geodesic ball)的纠缠熵在给定体积下是最大的,可以从量子纠缠第一定律推导出弗里德曼方程.研究表明引力与量子纠缠之间存在着某种深刻的联系,这种联系对引力场方程的解是成立的.

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