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Does gravity come from quantum information?

Abstract

Reconciling quantum mechanics with gravity has long posed a challenge for physicists. Recent developments have seen concepts originally developed in quantum information theory, such as entanglement and quantum error correction, come to play a fundamental role in understanding quantum gravity.

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Fig. 1: Schematic illustration of holographic duality and RT formula.
Fig. 2: Analogy between accessing bulk qubit from the boundary and quantum error correction.
Fig. 3: Tensor network state and the encoded bulk qubit.
Fig. 4: The relation between entanglement, bulk geometry and energy–momentum of the boundary.
Fig. 5: The scattering between two particles, a and b, near the black hole horizon.

References

  1. 1.

    Bekenstein, J. D. Black holes and the second law. Lett. Nuovo Cim. 4, 737–740 (1972).

    ADS  Article  Google Scholar 

  2. 2.

    Bekenstein, J. D. Black holes and entropy. Phys. Rev. D 7, 2333–2346 (1973).

    ADS  MathSciNet  Article  Google Scholar 

  3. 3.

    Hawking, S. W. Gravitational radiation from colliding black holes. Phys. Rev. Lett. 26, 1344–1346 (1971).

    ADS  Article  Google Scholar 

  4. 4.

    Hawking, S. W. Black hole explosions? Nature 248, 30–31 (1974).

    ADS  Article  Google Scholar 

  5. 5.

    Susskind, L. The world as a hologram. J. Math. Phys. 36, 6377–6396 (1995).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6.

    Bousso, R. The holographic principle. Rev. Mod. Phys. 74, 825–874 (2002).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7.

    ’t Hooft, G. Dimensional reduction in quantum gravity. Preprint at https://arxiv.org/abs/gr-qc/9310026 (1993).

  8. 8.

    Maldacena, J. The large-N limit of superconformal field theories and supergravity. Int. J. Theor. Phys. 38, 1113 (1999).

    MathSciNet  Article  Google Scholar 

  9. 9.

    Witten, E. Anti de Sitter space and holography. Adv. Theor. Math. Phys. 2, 253–291 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  10. 10.

    Gubser, S. S., Klebanov, I. R. & Polyakov, A. M. Gauge theory correlators from non-critical string theory. Phys. Lett. B 428, 105–114 (1998).

    ADS  MathSciNet  Article  Google Scholar 

  11. 11.

    Ryu, S. & Takayanagi, T. Holographic derivation of entanglement entropy from the anti–de Sitter space/conformal field theory correspondence. Phys. Rev. Lett. 96, 181602 (2006).

    ADS  MathSciNet  Article  Google Scholar 

  12. 12.

    Hubeny, V. E., Rangamani, M. & Takayanagi, T. A covariant holographic entanglement entropy proposal. J. High Energy Phys. 2007, 062 (2007).

    ADS  MathSciNet  Article  Google Scholar 

  13. 13.

    Faulkner, T., Lewkowycz, A. & Maldacena, J. Quantum corrections to holographic entanglement entropy. J. High Energy Phys. 2013, 074 (2013).

    Article  Google Scholar 

  14. 14.

    Van Raamsdonk, M. Building up spacetime with quantum entanglement. Gen. Relativ. Gravit. 42, 2323–2329 (2010).

    ADS  MathSciNet  Article  Google Scholar 

  15. 15.

    Maldacena, J. & Susskind, L. Cool horizons for entangled black holes. Fortschr. Phys. 61, 781–811 (2013).

    MathSciNet  Article  Google Scholar 

  16. 16.

    Hayden, P., Headrick, M. & Maloney, A. Holographic mutual information is monogamous. Phys. Rev. D 87, 046003 (2013).

    ADS  Article  Google Scholar 

  17. 17.

    Almheiri, A., Dong, X. & Harlow, D. Bulk locality and quantum error correction in AdS/CFT. J. High Energy Phys. 2015, 163 (2015).

    MathSciNet  Article  Google Scholar 

  18. 18.

    Hubeny, V. E. & Rangamani, M. Causal holographic information. J. High Energy Phys. 2012, 114 (2012).

    ADS  MathSciNet  Article  Google Scholar 

  19. 19.

    Headrick, M., Hubeny, V. E., Lawrence, A. & Rangamani, M. Causality & holographic entanglement entropy. J. High Energy Phys. 2014, 162 (2014).

    ADS  Article  Google Scholar 

  20. 20.

    Harlow, D. The Ryu–Takayanagi formula from quantum error correction. Commun. Math. Phys. 354, 865–912 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    Swingle, B. Entanglement renormalization and holography. Phys. Rev. D 86, 065007 (2012).

    ADS  Article  Google Scholar 

  22. 22.

    White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992).

    ADS  Article  Google Scholar 

  23. 23.

    Verstraete, F., Murg, V. & Cirac, J. I. Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems. Adv. Phys. 57, 143–224 (2008).

    ADS  Article  Google Scholar 

  24. 24.

    Vidal, G. Class of quantum many-body states that can be efficiently simulated. Phys. Rev. Lett. 101, 110501 (2008).

    ADS  Article  Google Scholar 

  25. 25.

    DiVincenzo, D. P. et al. in Quantum Computing and Quantum Communications (ed. Williams, C. P.) 247–257 (Springer, Berlin, 1999).

  26. 26.

    Pastawski, F., Yoshida, B., Harlow, D. & Preskill, J. Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence. J. High Energy Phys. 2015, 149 (2015).

    MathSciNet  Article  Google Scholar 

  27. 27.

    Yang, Z., Hayden, P. & Qi, X.-L. Bidirectional holographic codes and sub-AdS locality. J. High Energy Phys. 2016, 175 (2016).

    MathSciNet  Article  Google Scholar 

  28. 28.

    Hayden, P. et al. Holographic duality from random tensor networks. J. High Energy Phys. 2016, 9 (2016).

    MathSciNet  Article  Google Scholar 

  29. 29.

    Page, D. N. Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291–1294 (1993).

    ADS  MathSciNet  Article  Google Scholar 

  30. 30.

    Strominger, A. The dS/CFT correspondence. J. High Energy Phys. 2001, 034 (2001).

    MathSciNet  Article  Google Scholar 

  31. 31.

    Nomura, Y., Salzetta, N., Sanches, F. & Weinberg, S. J. Toward a holographic theory for general spacetimes. Phys. Rev. D 95, 086002 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  32. 32.

    Verlinde, E. Emergent gravity and the dark universe. SciPost Phys. 2, 016 (2017).

    Article  Google Scholar 

  33. 33.

    Han, M. & Huang, S. Discrete gravity on random tensor network and holographic Rényi entropy. J. High Energy Phys. 2017, 148 (2017).

    ADS  Article  Google Scholar 

  34. 34.

    Lashkari, N., McDermott, M. B. & Van Raamsdonk, M. Gravitational dynamics from entanglement “thermodynamics”. J. High Energy Phys. 2014, 195 (2014).

    Article  Google Scholar 

  35. 35.

    Swingle, B. & Van Raamsdonk, M. Universality of gravity from entanglement. Preprint at https://arxiv.org/abs/1405.2933 (2014).

  36. 36.

    Shenker, S. H. & Stanford, D. Black holes and the butterfly effect. J. High Energy Phys. 2014, 67 (2014).

    MathSciNet  Article  Google Scholar 

  37. 37.

    Larkin, A. & Ovchinnikov, Y. N. Quasiclassical method in the theory of superconductivity. J. Exp. Theor. Phys. 28, 1200–1205 (1969).

    ADS  Google Scholar 

  38. 38.

    Shenker, S. H. & Stanford, D. Stringy effects in scrambling. J. High Energy Phys. 2015, 132 (2015).

    MathSciNet  Article  Google Scholar 

  39. 39.

    Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High Energy Phys. 2016, 106 (2016).

    MathSciNet  Article  Google Scholar 

  40. 40.

    Sachdev, S. & Ye, J. Gapless spin-fluid ground state in a random quantum Heisenberg magnet. Phys. Rev. Lett. 70, 3339–3342 (1993).

    ADS  Article  Google Scholar 

  41. 41.

    Kitaev, A. A simple model of quantum holography. KITP http://online.kitp.ucsb.edu/online/entangled15/kitaev/; http://online.kitp.ucsb.edu/online/entangled15/kitaev2/ (2015).

  42. 42.

    Maldacena, J. & Stanford, D. Remarks on the Sachdev-Ye-Kitaev model. Phys. Rev. D 94, 106002 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  43. 43.

    Almheiri, A., Marolf, D., Polchinski, J. & Sully, J. Black holes: complementarity or firewalls? J. High Energy Phys. 2013, 62 (2013).

    MathSciNet  Article  Google Scholar 

  44. 44.

    Stanford, D. & Susskind, L. Complexity and shock wave geometries. Phys. Rev. D 90, 126007 (2014).

    ADS  Article  Google Scholar 

  45. 45.

    Brown, A. R., Roberts, D. A., Susskind, L., Swingle, B. & Zhao, Y. Holographic complexity equals bulk action? Phys. Rev. Lett. 116, 191301 (2016).

    ADS  Article  Google Scholar 

  46. 46.

    Susskind, L. Dear Qubitzers, GR=QM. Preprint at https://arxiv.org/abs/1708.03040 (2017).

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Acknowledgements

This work is supported by the National Science Foundation under grant no. 1720504.

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Correspondence to Xiao-Liang Qi.

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Qi, XL. Does gravity come from quantum information?. Nature Phys 14, 984–987 (2018). https://doi.org/10.1038/s41567-018-0297-3

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