TY - JOUR

T1 - Soft-Hair-Enhanced Entanglement beyond Page Curves in a Black Hole Evaporation Qubit Model

AU - Hotta, Masahiro

AU - Nambu, Yasusada

AU - Yamaguchi, Koji

N1 - Funding Information:
In a model of decaying qubits into zero-energy degrees of freedom, the thermal properties of 4-dim Schwarzschild BH evaporation are precisely reproduced. The EE is much larger than the average thermal entropy and the Bekenstein-Hawking entropy analogue for each qubit. This is the first result of a breakdown of the Page curve ansatz in a model which satisfies the Hawking temperature relation in Eq. (1) . The result provides a new feature for a resolution of the information loss problem. In our model, the emission of a Hawking particle of Ψ R at an early stage makes a transition from | + ⟩ into | - ⟩ of a qubit. After the Page time, the qubit in | - ⟩ almost decays into a zero-energy particle of Ψ S , which may be interpreted as BMS soft hair propagating to future null infinity. This suggests that, in the BH firewall paradox [23–25] , early Hawking radiation is entangled with zero-energy BMS soft hair and that late Hawking radiation can be highly entangled with the degrees of freedom of the BH (surviving qubits in | - ⟩ ), avoiding the emergence of a firewall at the horizon. The soft-hair influence for black holes with positive heat capacity like large AdS black holes remains elusive. The authors thank Masanori Hanada and Hal Tasaki for useful discussions. This research was partially supported by Kakenhi Grants-in-Aid [No. 16K05311 (M. H.) and No. 16H01094 (Y. N.)] from the Japan Society for the Promotion of Science (JSPS) and by the Tohoku University Graduate Program on Physics for the Universe (K. Y.). [1] 1 S. Ryu and T. Takayanagi , Phys. Rev. Lett. 96 , 181602 ( 2006 ). PRLTAO 0031-9007 10.1103/PhysRevLett.96.181602 [2] 2 T. Jacobson , Phys. Rev. Lett. 116 , 201101 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.201101 [3] 3 A. Kitaev and J. Preskill , Phys. Rev. Lett. 96 , 110404 ( 2006 ). PRLTAO 0031-9007 10.1103/PhysRevLett.96.110404 [4] 4 M. Levin and X.-G. Wen , Phys. Rev. Lett. 96 , 110405 ( 2006 ). PRLTAO 0031-9007 10.1103/PhysRevLett.96.110405 [5] 5 R. Islam , R. Ma , P. M. Preiss , M. E. Tai , A. Lukin , M. Rispoli , and M. Greiner , Nature (London) 528 , 77 ( 2015 ). NATUAS 0028-0836 10.1038/nature15750 [6] 6 S. W. Hawking , Commun. Math. Phys. 43 , 199 ( 1975 ). CMPHAY 0010-3616 10.1007/BF02345020 [7] 7 S. W. Hawking , Phys. Rev. D 72 , 084013 ( 2005 ). PRVDAQ 1550-7998 10.1103/PhysRevD.72.084013 [8] 8 D. N. Page , Phys. Rev. Lett. 71 , 3743 ( 1993 ). PRLTAO 0031-9007 10.1103/PhysRevLett.71.3743 [9] 9 M. Hotta , K. Sasaki , and T. Sasaki , Classical Quantum Gravity 18 , 1823 ( 2001 ). CQGRDG 0264-9381 10.1088/0264-9381/18/10/301 [10] 10 S. W. Hawking , M. J. Perry , and A. Strominger , Phys. Rev. Lett. 116 , 231301 ( 2016 ). PRLTAO 0031-9007 10.1103/PhysRevLett.116.231301 [11] 11 M. Hotta , J. Trevison , and K. Yamaguchi , Phys. Rev. D 94 , 083001 ( 2016 ). PRVDAQ 2470-0010 10.1103/PhysRevD.94.083001 [12] 12 S. W. Hawking , M. J. Perry , and A. Strominger , J. High Energy Phys. 05 ( 2017 ) 161 . JHEPFG 1029-8479 10.1007/JHEP05(2017)161 [13] 13 E. Berkowitz , M. Hanada , and J. Maltz , Phys. Rev. D 94 , 126009 ( 2016 ). PRVDAQ 2470-0010 10.1103/PhysRevD.94.126009 [14] 14 S. D. Mathur , Classical Quantum Gravity 26 , 224001 ( 2009 ). CQGRDG 0264-9381 10.1088/0264-9381/26/22/224001 [15] 15 S. B. Giddings , Phys. Rev. D 85 , 124063 ( 2012 ). PRVDAQ 1550-7998 10.1103/PhysRevD.85.124063 [16] 16 S. G. Avery , J. High Energy Phys. 01 ( 2013 ) 176 . JHEPFG 1029-8479 10.1007/JHEP01(2013)176 [17] 17 E. Lubkin , J. Math. Phys. (N.Y.) 19 , 1028 ( 1978 ). JMAPAQ 0022-2488 10.1063/1.523763 [18] 18 S. Lloyd and H. Pagels , Ann. Phys. (N.Y.) 188 , 186 ( 1988 ). APNYA6 0003-4916 10.1016/0003-4916(88)90094-2 [19] 19 A. Sugita , RIMS Kokyuroku (Kyoto) 1507 , 147 ( 2006 ). 1880-2818 [20] 20 A. Sugita , Nonlinear Phenom. Complex Syst. 10 , 192 ( 2007 ). NPCSFD 1386-288X [21] 21 Y. Sekino and L. Susskind , J. High Energy Phys. 10 ( 2008 ) 065 . JHEPFG 1029-8479 10.1088/1126-6708/2008/10/065 [22] 22 See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.120.181301 for more detailed derivations. [23] 23 S. L. Braunstein , S. Pirandola , and K. Życzkowski , Phys. Rev. Lett. 110 , 101301 ( 2013 ). PRLTAO 0031-9007 10.1103/PhysRevLett.110.101301 [24] 24 A. Almheiri , D. Marolf , J. Polchinski , and J. Sully , J. High Energy Phys. 02 ( 2013 ) 062 . JHEPFG 1029-8479 10.1007/JHEP02(2013)062 [25] 25 M. Hotta and A. Sugita , Prog. Theor. Exp. Phys. 2015 , 123B04 ( 2015 ). PTEPCR 2050-3911 10.1093/ptep/ptv170
Publisher Copyright:
© 2018 American Physical Society.

PY - 2018/5/4

Y1 - 2018/5/4

N2 - We propose a model with multiple qubits that reproduces the thermal properties of four-dimensional Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft-hair evaporation at the horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair and that late Hawking radiation can be highly entangled with the degrees of freedom of a BH, avoiding the emergence of a firewall at the horizon.

AB - We propose a model with multiple qubits that reproduces the thermal properties of four-dimensional Schwarzschild black holes (BHs) by simultaneously taking account of the emission of Hawking particles and the zero-energy soft-hair evaporation at the horizon. The results verify that the entanglement entropy between a qubit and other subsystems, including emitted radiation, is much larger than the BH entropy analogue of the qubit, as opposed to the Page curve prediction. Our result suggests that early Hawking radiation is entangled with soft hair and that late Hawking radiation can be highly entangled with the degrees of freedom of a BH, avoiding the emergence of a firewall at the horizon.

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U2 - 10.1103/PhysRevLett.120.181301

DO - 10.1103/PhysRevLett.120.181301

M3 - Article

C2 - 29775375

AN - SCOPUS:85046541078

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 18

M1 - 181301

ER -