2014

Entanglement is not Enough

Susskind, Leonard

Understand

This is the written version of a lecture given at KITP in Oct 2014 on Black Holes and quantum complexity.

I've included (in boldface) various questions that came up during the lecture and discussions the following day, as well as the quantitative calculations that form the basis of the arguments.

Built on

R. P. Feynman, “Simulating physics with computers,” Int. J. Theor. Phys. 21
1982
Earlier work this paper cites.
D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
L. Susskind, L. Thorlacius and J. Uglum, “The Stretched horizon and black hole complementarity,” Phys. Rev. D 48
1993
Earlier work this paper cites.
D. Garfinkle and A. Strominger, “Semiclassical Wheeler wormhole production,” Phys. Lett. B 256
1994
Earlier work this paper cites.
L. Susskind and L. Thorlacius, “Gedanken experiments involving black holes,” Phys. Rev. D 49
1994
Earlier work this paper cites.
J. M. Maldacena and L. Susskind, “D-branes and fat black holes,” Nucl. Phys. B 475
1996
Earlier work this paper cites.

Similar

R. Bousso, “A Covariant entropy conjecture,” JHEP 9907
1999
Cited alongside, same era.
J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 0304
2003
Cited alongside, same era.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP 0709
Original
2007
Cited alongside, same era.
D. Harlow and P. Hayden, “Quantum Computation vs. Firewalls,” arXiv:1301.4504 [hep-th]. S. L. Braunstein, “Black hole entropy as entropy of entanglement, or it’s curtains for the equivalence principle”, arXiv:0907.1190v1 [quant-ph]. S. D. Mathur, “The Information paradox: A Pedagogical introduction,” Class. Quant. Grav. 26
Original
2009
Cited alongside, same era.
M. Van Raamsdonk, “Building up spacetime with quantum entanglement,” Gen. Rel. Grav. 42
Original
2010
Cited alongside, same era.
G. Evenbly and G. Vidal, Tensor network states and geometry, J. Stat. Phys. 145, 891 (2011). [arXiv: 1106.1082 [quant-ph]]
2011
Cited alongside, same era.
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” arXiv:1306.0533 [hep-th]
Original
Cited in the paper.
L. Susskind, “Computational Complexity and Black Hole Horizons,” arXiv:1402.5674 [hep-th]
Original
Cited in the paper.
D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” arXiv:1406.2678 [hep-th]
Original
Cited in the paper.
L. Susskind and Y. Zhao, “Switchbacks and the Bridge to Nowhere,” arXiv:1408.2823 [hep-th]
Original
Cited in the paper.
D. A. Roberts, D. Stanford and L. Susskind, “Localized shocks,” arXiv:1409.8180 [hep-th]
Original
Cited in the paper.
Michael A. Nielsen, “A geometric approach to quantum circuit lower bounds” arXiv:quant-ph/0502070 Mark R. Dowling, Michael A. Nielsen, “The geometry of quantum computation” arXiv:quant-ph/0701004
Cited in the paper.

Then

A. Almheiri, D. Marolf, J. Polchinski and J. Sully, “Black Holes: Complementarity or Firewalls?,” JHEP 1302
Original
2013
Later among the works it cites.
D. Marolf and J. Polchinski, “Gauge/Gravity Duality and the Black Hole Interior,” Phys. Rev. Lett. 111
Original
2013
Later among the works it cites.
T. Hartman and J. Maldacena, “Time Evolution of Entanglement Entropy from Black Hole Interiors,” JHEP 1305
Original
2014
Closest in time.
S. H. Shenker and D. Stanford, JHEP 1403
Original
2014
Closest in time.
V. Balasubramanian, P. Hayden, A. Maloney, D. Marolf and S. F. Ross, “Multiboundary Wormholes and Holographic Entanglement,” Class. Quant. Grav. 31
Original
2014
Closest in time.

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