Fetching the paper…

Reading the bibliography…

2014

Complexity and Shock Wave Geometries

Stanford, Douglas, Susskind, Leonard

Original
PDF
Post on X

Understand

In this paper we refine a conjecture relating the time-dependent size of an Einstein-Rosen bridge to the computational complexity of the of the dual quantum state.

Our refinement states that the complexity is proportional to the spatial volume of the ERB.
More precisely, up to an ambiguous numerical coefficient, we propose that the complexity is the regularized volume of the largest codimension one surface crossing the bridge, divided by $G_N l_{AdS}$.
We test this conjecture against a wide variety of spherically symmetric shock wave geometries in different dimensions.

Complexity and Shock Wave Geometries · Around

Built on

T. Dray and G. ’t Hooft, “The Effect of Spherical Shells of Matter on the Schwarzschild Black Hole,” Commun. Math. Phys. 99
1985
Earlier work this paper cites.
J. Louko, D. Marolf and S. F. Ross, “On geodesic propagators and black hole holography,” Phys. Rev. D 62
2000
Earlier work this paper cites.
P. Kraus, H. Ooguri and S. Shenker, “Inside the horizon with AdS / CFT,” Phys. Rev. D 67
2003
Earlier work this paper cites.
J. M. Maldacena, “Eternal black holes in anti-de Sitter,” JHEP 0304
2003
Earlier work this paper cites.
L. Fidkowski, V. Hubeny, M. Kleban and S. Shenker, “The Black hole singularity in AdS / CFT,” JHEP 0402
2004
Earlier work this paper cites.

Similar

S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
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.
M. Van Raamsdonk, “Evaporating Firewalls,” arXiv:1307.1796 [hep-th]. B. Czech, J. L. Karczmarek, F. Nogueira and M. Van Raamsdonk, “Rindler Quantum Gravity,” Class. Quant. Grav. 29
Original
2012
Cited alongside, same era.
E. Knill, “Approximation by quantum circuits,” quant-ph/9508006
Cited in the paper.
D. Harlow and P. Hayden, “Quantum Computation vs. Firewalls,” arXiv:1301.4504 [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.
S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,” arXiv:1306.0622 [hep-th]
Original
Cited in the paper.
S. H. Shenker and D. Stanford, “Multiple Shocks,” arXiv:1312.3296 [hep-th]
Original
Cited in the paper.
L. Susskind, “Addendum to Computational Complexity and Black Hole Horizons,” arXiv:1403.5695 [hep-th]
Original
Cited in the paper.
J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” arXiv:1306.0533 [hep-th]
Original
Cited in the paper.
M. Dowling, M. Nielsen, “The geometry of quantum computation,” arXiv:quant-ph/0701004
Cited in the paper.

Then

B. Swingle, “Entanglement Renormalization and Holography,” Phys. Rev. D 86
Original
2012
Later among the works it cites.
I. Heemskerk, D. Marolf, J. Polchinski and J. Sully, “Bulk and Transhorizon Measurements in AdS/CFT,” JHEP 1210
Original
2012
Later among the works it cites.
T. Hartman and J. Maldacena, “Time Evolution of Entanglement Entropy from Black Hole Interiors,” JHEP 1305
Original
2013
Later among the works it cites.
H. Liu and S. J. Suh, “Entanglement Tsunami: Universal Scaling in Holographic Thermalization,” Phys. Rev. Lett. 112
Original
2014
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…