量子纠缠与时空结构

doi:10.3969/j.issn.0253-9608.2023.05.012

自然杂志 ›› 2023, Vol. 45 ›› Issue (6): 455-462.doi: 10.3969/j.issn.0253-9608.2023.05.012

量子纠缠与时空结构

林淑怡，葛先辉，田立君

上海大学理学院物理系，上海 200444

收稿日期:2023-02-16 出版日期:2023-12-25 发布日期:2023-12-22
通讯作者: 葛先辉，研究方向：引力与黑洞物理、引力/规范场应用、类比引力、强关联体系输运性质和相变。
基金资助:
国家自然科学基金项目(12275166、11875184)

Quantum entanglement and spacetime structure

LIN Shuyi, GE Xianhui, TIAN Lijun

Department of Physics, College of Sciences, Shanghai University, Shanghai 200444, China

Received:2023-02-16 Online:2023-12-25 Published:2023-12-22

摘要/Abstract

摘要： 众所周知，自然界中存在着四种基本相互作用，分别为强相互作用、弱相互作用、电磁相互作用与引力相互作用。然而，前三者可以在量子力学的框架下自洽，只有特殊的引力相互作用尚未与其他相互作用统一。因此，追求引力的量子化是现代物理学最迫切和首要的目标。物理学家们发现，可以利用量子场论的方法来研究引力理论。在这过程中，我们发现量子纠缠、几何以及时空定域性之间的关系，这似乎暗示了通往量子引力的研究方向。通过量子纠缠，我们希望进一步探索量子引力领域，为引力的量子化找到一个突破口，从而发现时空的本质。文章简要回顾量子纠缠熵的历史发展，并讨论纠缠熵与几何之间的关系。

关键词: 纠缠熵, 量子纠缠, 佩奇曲线, AdS/CFT对偶, 量子极值面

Abstract: We review recent progresses on entanglement entropy and Page curve of black holes, and discuss the relationship between entanglement entropy and geometry. As is well-known, there are four fundamental interactions in nature: the strong interaction, the weak interaction, the electromagnetic interaction, and gravity. However, the first three interactions have already been unified by quantum theory, with only gravity remaining as a separate theory from the others. Therefore, the most important objective of modern physics is to study the theory of quantum gravity. Physicists have found that they can use quantum field theory to study gravity. In this process, we can discover the relationships among quantum entanglement, geometry, and the localization of spacetime, which implies the direction of the development of quantum gravity. We hope to find a breakthrough in the quantization of gravity through quantum entanglement. We then are able to explore the nature of quantum gravity and further understand the nature of spacetime.

林淑怡, 葛先辉, 田立君. 量子纠缠与时空结构[J]. 自然杂志, 2023, 45(6): 455-462.

LIN Shuyi, GE Xianhui, TIAN Lijun. Quantum entanglement and spacetime structure[J]. Chinese Journal of Nature, 2023, 45(6): 455-462.

参考文献

[1] EINSTEIN A, PODOLSKY B, ROSEN N. Can quantum-mechanical description of physical reality be considered complete? [J]. Phys
Rev, 1935, 47(10): 777-780.
[2] BELL J S. On the Einstein Podolsky Rosen paradox [J]. Physics, 1964, 1(3): 195-200.
[3] ASPECT A, GRANGIER P, ROGER G. Experimental realization of Einstein-Podolsky-Rosen-Bohm gedankenexperiment: a new
violation of Bell’s inequalities [J]. Phys Rev Lett, 1982, 49(2): 91-94.
[4] KYSELA J, ERHARD M, HOCHRAINER A, et al. Path identity as a source of high-dimensional entanglement [J]. Proc Natl Acad Sci
USA, 2020, 117(42): 26118-26122.
[5] SHANNON C E. A mathematical theory of communication [J]. Bell Syst Tech J, 1948, 27(3): 379-423.
[6] KULLBACK S, LEIBLER R A. On information and sufficiency [J]. Ann Math Statist, 1951, 22(1): 79-86.
[7] BENNETT C H, DIVINCENZO D P, SMOLIN J A, et al. Mixedstate entanglement and quantum error correction [J]. Phys Rev A,
1996, 54(5): 3824-3851.
[8] VIDAL G, WERNER R F. Computable measure of entanglement [J]. Phys Rev A, 2002, 65(3): 032314.
[9] HEADRICK M. Lectures on entanglement entropy in field theory and holography BRX-TH-6653[R/OL]. [2023-2-16]. https://arxiv.
org/abs/1907.08126.
[10] PAGE D N. Information in black hole radiation [J]. Phys Rev Lett, 1993, 71(23): 3743-3746.
[11] SUSSKIND L. The world as a hologram [J]. J Math Phys, 1995, 36(11): 6377-6396.
[12] MALDACENA J. The large-N limit of superconformal field theories and supergravity [J]. Int J Theor Phys, 1999, 38(4): 1113-1133.
[13] MARTIN A, JOHANNA E. Gauge/gravity duality foundations and applications [M]. Cambridge: Cambridge University Press, 2015.
[14] WITTEN E. Anti de sitter space and holography [J]. Adv Theor Math Phys, 1998, 2(2): 253-291.
[15] GUBSER S S, KLEBANOV I R, POLYAKOV A M. Gauge theory correlators from non-critical string theory [J]. Phys Lett B, 1998,
428(1/2): 105-114.
[16] RYU S, TAKAYANAGI T. Holographic derivation of entanglement entropy from AdS/CFT [J]. Phys Rev Lett, 2006, 96: 181602.
[17] HAWKING S, ELLIS G F R. The large scale structure of space-time[M]. Cambridge: University Press, 1973.
[18] BEKENSTEIN J D. Black holes and entropy [J]. Phys Rev D, 1973, 7(8): 2333-2346.
[19] ALMHEIRI A, DONG X, HARLOW D. Bulk locality and quantum error correction in AdS/CFT [J]. J High Energ Phys, 2015, 2015(4):
163.
[20] HUBENY V E, RANGAMANI M. Causal holographic information [J]. J High Energ Phys, 2012, 2012(6): 114.
[21] HEADRICK M, HUBENY V E, LAWRENCE A, et al. Causality & holographic entanglement entropy [J]. J High Energ Phys, 2014,
2014(12): 162.
[22] HARLOW D. The Ryu-Takayanagi formula from quantum error correction [J]. Commun Math Phys, 2017, 354(3): 865-912.
[23] QI X L. Does gravity come from quantum information? [J]. Nat Phys, 2018, 14(10): 984-987.
[24] NISHIOKA T. Entanglement entropy: holography and renormalization group [J]. Rev Mod Phys, 2018, 90(3): 035007.
[25] FAULKNER T, LEWKOWYCZ A, MALDACENA J. Quantum corrections to holographic entanglement entropy [J]. J High Energ
Phys, 2013, 2013(11): 74.
[26] ENGELHARDT N, WALL A C. Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime [J]. J High Energ Phys, 2015, 2015(1): 73.
[27] PAGE D N. Information in black hole radiation [J]. Phys Rev Lett, 1993, 71(23): 3743-3746.
[28] PENINGTON G. Entanglement wedge reconstruction and the information paradox [J]. J High Energ Phys, 2020, 2020(9): 2.
[29] ALMHEIRI A, ENGELHARDT N, MAROLF D, et al. The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole [J]. J High Energ Phys, 2019, 2019(12): 63.
[30] ALMHEIRI A, MAHAJAN R, MALDACENA J, et al. The Page curve of Hawking radiation from semiclassical geometry [J]. J High
Energ Phys, 2020, 2020(3): 149.
[31] HARTMAN T, SHAGHOULIAN E, STROMINGER A. Islands in asymptotically flat 2D gravity [J]. J High Energ Phys, 2020,
2020(7): 22.
[32] YU M H, GE X H. Entanglement islands in generalized twodimensional dilaton black holes [J]. Phys Rev D, 2023, 107(6):
066020.
[33] KARANANAS G K, KEHAGIAS A, TASKAS J. Islands in linear dilaton black holes [J]. J High Energ Phys, 2021, 2021(3): 253.

量子纠缠与时空结构

Quantum entanglement and spacetime structure

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	施郁. 量子纠缠之路：从爱因斯坦到2022年诺贝尔物理学奖[J]. 自然杂志, 2022, 44(6): 455-465.
[2]	余明辉, 葛先辉. 黑洞信息佯谬：落入黑洞的信息丢失了吗？[J]. 自然杂志, 2021, 43(2): 127-134.
[3]	施郁. 揭秘量子密码、量子纠缠与量子隐形传态[J]. 自然杂志, 2016, 38(4): 241-247.