Abstract
Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this paper, we investigate such constraints arising from strong subadditivity and from the positivity and monotonicity of relative entropy in examples with highly-symmetric spacetimes. Our results may be interpreted as a set of energy conditions restricting the possible form of the stress-energy tensor in consistent theories of Einstein gravity coupled to matter.
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J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large-N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
V.E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 07 (2007) 062 [arXiv:0705.0016] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
P. Hayden, M. Headrick and A. Maloney, Holographic mutual information is monogamous, Phys. Rev. D 87 (2013) 046003 [arXiv:1107.2940] [INSPIRE].
J. Hammersley, Extracting the bulk metric from boundary information in asymptotically AdS spacetimes, JHEP 12 (2006) 047 [hep-th/0609202] [INSPIRE].
S. Bilson, Extracting spacetimes using the AdS/CFT conjecture, JHEP 08 (2008) 073 [arXiv:0807.3695] [INSPIRE].
V. Balasubramanian, B.D. Chowdhury, B. Czech, J. de Boer and M.P. Heller, Bulk curves from boundary data in holography, Phys. Rev. D 89 (2014) 086004 [arXiv:1310.4204] [INSPIRE].
N. Lashkari, M.B. McDermott and M. Van Raamsdonk, Gravitational dynamics from entanglement “thermodynamics”, JHEP 04 (2014) 195 [arXiv:1308.3716] [INSPIRE].
T. Faulkner, M. Guica, T. Hartman, R.C. Myers and M. Van Raamsdonk, Gravitation from entanglement in holographic CFTs, JHEP 03 (2014) 051 [arXiv:1312.7856] [INSPIRE].
B. Swingle and M. Van Raamsdonk, Universality of gravity from entanglement, arXiv:1405.2933 [INSPIRE].
M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, Dynamics of entanglement entropy from Einstein equation, Phys. Rev. D 88 (2013) 026012 [arXiv:1304.7100] [INSPIRE].
J. Bhattacharya and T. Takayanagi, Entropic counterpart of perturbative Einstein equation, JHEP 10 (2013) 219 [arXiv:1308.3792] [INSPIRE].
S. Banerjee, A. Kaviraj and A. Sinha, Nonlinear constraints on gravity from entanglement, Class. Quant. Grav. 32 (2015) 065006 [arXiv:1405.3743] [INSPIRE].
S. Banerjee, A. Bhattacharyya, A. Kaviraj, K. Sen and A. Sinha, Constraining gravity using entanglement in AdS/CFT, JHEP 05 (2014) 029 [arXiv:1401.5089] [INSPIRE].
R.C. Myers and A. Singh, Comments on holographic entanglement entropy and RG flows, JHEP 04 (2012) 122 [arXiv:1202.2068] [INSPIRE].
R. Callan, J.-Y. He and M. Headrick, Strong subadditivity and the covariant holographic entanglement entropy formula, JHEP 06 (2012) 081 [arXiv:1204.2309] [INSPIRE].
A.C. Wall, Maximin surfaces and the strong subadditivity of the covariant holographic entanglement entropy, Class. Quant. Grav. 31 (2014) 225007 [arXiv:1211.3494] [INSPIRE].
E. Caceres, A. Kundu, J.F. Pedraza and W. Tangarife, Strong subadditivity, null energy condition and charged black holes, JHEP 01 (2014) 084 [arXiv:1304.3398] [INSPIRE].
D.D. Blanco, H. Casini, L.-Y. Hung and R.C. Myers, Relative entropy and holography, JHEP 08 (2013) 060 [arXiv:1305.3182] [INSPIRE].
J. Lin, M. Marcolli, H. Ooguri and B. Stoica, Tomography from entanglement, arXiv:1412.1879 [INSPIRE].
M.A. Nielsen and I.L. Chuang, Quantum computation and quantum information, Cambridge University Press, Cambridge U.K. (2010).
M. Headrick and T. Takayanagi, A holographic proof of the strong subadditivity of entanglement entropy, Phys. Rev. D 76 (2007) 106013 [arXiv:0704.3719] [INSPIRE].
J. Bhattacharya, V.E. Hubeny, M. Rangamani and T. Takayanagi, Entanglement density and gravitational thermodynamics, Phys. Rev. D 91 (2015) 106009 [arXiv:1412.5472] [INSPIRE].
H. Casini and M. Huerta, A finite entanglement entropy and the c-theorem, Phys. Lett. B 600 (2004) 142 [hep-th/0405111] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
B. Swingle and I.H. Kim, Reconstructing quantum states from local data, Phys. Rev. Lett. 113 (2014) 260501 [arXiv:1407.2658] [INSPIRE].
M. Parikh and J.P. van der Schaar, Derivation of the null energy condition, Phys. Rev. D 91 (2015) 084002 [arXiv:1406.5163] [INSPIRE].
T. Faulkner, A. Lewkowycz and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 11 (2013) 074 [arXiv:1307.2892] [INSPIRE].
M. Headrick, R.C. Myers and J. Wien, Holographic holes and differential entropy, JHEP 10 (2014) 149 [arXiv:1408.4770] [INSPIRE].
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ArXiv ePrint: 1412.3514
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Lashkari, N., Rabideau, C., Sabella-Garnier, P. et al. Inviolable energy conditions from entanglement inequalities. J. High Energ. Phys. 2015, 67 (2015). https://doi.org/10.1007/JHEP06(2015)067
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DOI: https://doi.org/10.1007/JHEP06(2015)067