Built on

B. Freivogel, V. Godet, E. Morvan, J. F. Pedraza, and A. Rotundo, Lessons on Eternal Traversable Wormholes in AdS, J. High Energy Phys. 07
Original
1903
Earlier work this paper cites.
A. Romero-Bermúdez, K. Schalm, and V. Scopelliti, Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?, JHEP 07
Original
1903
Earlier work this paper cites.
Z. Fu, B. Grado-White, and D. Marolf, Traversable Asymptotically Flat Wormholes with Short Transit Times, Class. Quant. Grav. 36
Original
1908
Earlier work this paper cites.
D. Marolf and S. McBride, Simple Perturbatively Traversable Wormholes from Bulk Fermions, J. High Energy Phys. 11
Original
1908
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, Sov. Phys. JETP 28
1969
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B428
1998
Earlier work this paper cites.
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 2007
Original
2007
Earlier work this paper cites.
H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states, Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80
2008
Earlier work this paper cites.
M. van Raamsdonk, Building up spacetime with quantum entanglement, General Relativity and Gravitation 42
Original
2010
Earlier work this paper cites.
U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (N. Y). 326
Original
2011
Earlier work this paper cites.
W. Brown and O. Fawzi, Scrambling speed of random quantum circuits, arXiv:1210.6644 [quant-ph] (2012)
Original
2012
Earlier work this paper cites.
B. Czech, J. L. Karczmarek, F. o. Nogueira, and M. Van Raamsdonk, The gravity dual of a density matrix, Classical and Quantum Gravity 29
Original
2012
Earlier work this paper cites.
R. Bousso, S. Leichenauer, and V. Rosenhaus, Light-sheets and AdS/CFT, Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
T. Faulkner, A. Lewkowycz, and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 2013
Original
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90
Original
2014
Earlier work this paper cites.

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S. H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 2014
2014
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S. Sachdev, Bekenstein-hawking entropy and strange metals, Phys. Rev. X 5
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A. Kitaev, A simple model of quantum holography, in KITP Progr. Entanglement Strongly-Correlated Quantum Matter (2015)
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D. A. Roberts, D. Stanford, and L. Susskind, Localized shocks, JHEP 2015
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2015
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Original
2015
Cited alongside, same era.

Then

J. Maldacena, D. Stanford, and Z. Yang, Diving into traversable wormholes, Fortsch. Phys. 65
Original
2017
Later among the works it cites.
M. Mezei and D. Stanford, On entanglement spreading in chaotic systems, JHEP 2017
Original
2017
Later among the works it cites.
A. Nahum, J. Ruhman, S. Vijay, and J. Haah, Quantum Entanglement Growth under Random Unitary Dynamics, Phys. Rev. X 7
2017
Later among the works it cites.
S. Kundu and J. F. Pedraza, Spread of entanglement for small subsystems in holographic CFTs, Phys. Rev. D95
Original
2017
Later among the works it cites.
C. D. White, M. Zaletel, R. S. K. Mong, and G. Refael, Quantum dynamics of thermalizing systems, Phys. Rev. B 97
Original

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2019

The Speed of Quantum Information Spreading in Chaotic Systems

Couch, Josiah, Eccles, Stefan, Nguyen, Phuc et al.

Understand

We present a general theory of quantum information propagation in chaotic quantum many-body systems.

The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements.
To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state.
As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed.

Built on

B. Freivogel, V. Godet, E. Morvan, J. F. Pedraza, and A. Rotundo, Lessons on Eternal Traversable Wormholes in AdS, J. High Energy Phys. 07
Original
1903
Earlier work this paper cites.
A. Romero-Bermúdez, K. Schalm, and V. Scopelliti, Regularization dependence of the OTOC. Which Lyapunov spectrum is the physical one?, JHEP 07
Original
1903
Earlier work this paper cites.
Z. Fu, B. Grado-White, and D. Marolf, Traversable Asymptotically Flat Wormholes with Short Transit Times, Class. Quant. Grav. 36
Original
1908
Earlier work this paper cites.
D. Marolf and S. McBride, Simple Perturbatively Traversable Wormholes from Bulk Fermions, J. High Energy Phys. 11
Original
1908
Earlier work this paper cites.
A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical Method in the Theory of Superconductivity, Sov. Phys. JETP 28
1969
Earlier work this paper cites.
J. M. Maldacena, The Large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38
1998
Earlier work this paper cites.
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2
1998
Earlier work this paper cites.
S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B428
1998
Earlier work this paper cites.
A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96
2006
Earlier work this paper cites.
G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 2007
Original
2007
Earlier work this paper cites.
H. Li and F. D. M. Haldane, Entanglement spectrum as a generalization of entanglement entropy: Identification of topological order in non-abelian fractional quantum hall effect states, Phys. Rev. Lett. 101
2008
Earlier work this paper cites.
L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80
2008
Earlier work this paper cites.
M. van Raamsdonk, Building up spacetime with quantum entanglement, General Relativity and Gravitation 42
Original
2010
Earlier work this paper cites.
U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (N. Y). 326
Original
2011
Earlier work this paper cites.
W. Brown and O. Fawzi, Scrambling speed of random quantum circuits, arXiv:1210.6644 [quant-ph] (2012)
Original
2012
Earlier work this paper cites.
B. Czech, J. L. Karczmarek, F. o. Nogueira, and M. Van Raamsdonk, The gravity dual of a density matrix, Classical and Quantum Gravity 29
Original
2012
Earlier work this paper cites.
R. Bousso, S. Leichenauer, and V. Rosenhaus, Light-sheets and AdS/CFT, Phys. Rev. D 86
Original
2012
Earlier work this paper cites.
T. Faulkner, A. Lewkowycz, and J. Maldacena, Quantum corrections to holographic entanglement entropy, JHEP 2013
Original
2013
Earlier work this paper cites.
D. Stanford and L. Susskind, Complexity and Shock Wave Geometries, Phys. Rev. D 90
Original
2014
Earlier work this paper cites.

Similar

S. H. Shenker and D. Stanford, Black holes and the butterfly effect, JHEP 2014
2014
Cited alongside, same era.
S. Sachdev, Bekenstein-hawking entropy and strange metals, Phys. Rev. X 5
2015
Cited alongside, same era.
A. Kitaev, A simple model of quantum holography, in KITP Progr. Entanglement Strongly-Correlated Quantum Matter (2015)
2015
Cited alongside, same era.
D. A. Roberts, D. Stanford, and L. Susskind, Localized shocks, JHEP 2015
Original
2015
Cited alongside, same era.
T. Hartman and N. Afkhami-Jeddi, Speed Limits for Entanglement, arXiv:1512.02695 [hep-th] (2015)
Original
2015
Cited alongside, same era.