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V. Alba, J. Dubail, and M. Medenjak, Phys. Rev. Lett. 122
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1901
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Y. Kusuki and M. Miyaji, Journal of High Energy Physics 2019
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J. Kudler-Flam, M. Nozaki, S. Ryu, and M. T. Tan, Journal of High Energy Physics 2020
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B. Craps, M. De Clerck, D. Janssens, V. Luyten, and C. Rabideau, arXiv e-prints , arXiv:1908.08059 (2019), arXiv:1908.08059 [hep-th]
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1909
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J. Kudler-Flam, L. Nie, and S. Ryu, Journal of High Energy Physics 2020
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1999
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1999
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J. Kudler-Flam, Y. Kusuki, and S. Ryu, JHEP 04
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2001
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S. de Haro, K. Skenderis, and S. N. Solodukhin, Communications in Mathematical Physics 217
2001
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2002
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2004
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2020

Entanglement of Local Operators and the Butterfly Effect

Kudler-Flam, Jonah, Nozaki, Masahiro, Ryu, Shinsei et al.

Understand

We study the robustness of quantum and classical information to perturbations implemented by local operator insertions.

We do this by computing multipartite entanglement measures in the Hilbert space of local operators in the Heisenberg picture.
The sensitivity to initial conditions that we explore is an illuminating manifestation of the butterfly effect in quantum many-body systems.
We derive a "membrane theory" in Haar random unitary circuits to compute the mutual information, logarithmic negativity, and reflected entropy in the local operator state by mapping to a classical statistical mechanics problem and find that any local operator insertion delocalizes information as fast as is allowed by causality.

Built on

V. Alba, J. Dubail, and M. Medenjak, Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
Y. Kusuki and M. Miyaji, Journal of High Energy Physics 2019
Original
1905
Earlier work this paper cites.
N. Hunter-Jones, arXiv e-prints , arXiv:1905.12053 (2019), arXiv:1905.12053 [quant-ph]
Original
1905
Earlier work this paper cites.
S. Dutta and T. Faulkner, arXiv e-prints , arXiv:1905.00577 (2019), arXiv:1905.00577 [hep-th]
Original
1905
Earlier work this paper cites.
J. Kudler-Flam, M. Nozaki, S. Ryu, and M. T. Tan, Journal of High Energy Physics 2020
Original
1906
Earlier work this paper cites.
H. Wang and T. Zhou, arXiv e-prints , arXiv:1907.09581 (2019), arXiv:1907.09581 [hep-th]
Original
1907
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, arXiv e-prints , arXiv:1907.06646 (2019a), arXiv:1907.06646 [hep-th]
Original
1907
Earlier work this paper cites.
B. Craps, M. De Clerck, D. Janssens, V. Luyten, and C. Rabideau, arXiv e-prints , arXiv:1908.08059 (2019), arXiv:1908.08059 [hep-th]
Original
1908
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, arXiv e-prints , arXiv:1909.07407 (2019a), arXiv:1909.07407 [cond-mat.stat-mech]
Original
1909
Earlier work this paper cites.
B. Bertini, P. Kos, and T. Prosen, arXiv e-prints , arXiv:1909.07410 (2019b), arXiv:1909.07410 [cond-mat.stat-mech]
Original
1909
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, Journal of High Energy Physics 2020
Original
1909
Earlier work this paper cites.
Y. Kusuki and K. Tamaoka, arXiv e-prints , arXiv:1909.06790 (2019b), arXiv:1909.06790 [hep-th]
Original
1909
Earlier work this paper cites.
J. Kudler-Flam, L. Nie, and S. Ryu, Journal of High Energy Physics 2020
Original
1910
Earlier work this paper cites.
L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen, Phys. Rev. B 101
Original
1911
Earlier work this paper cites.
M. Mezei and J. Virrueta, arXiv e-prints , arXiv:1912.11024 (2019), arXiv:1912.11024 [hep-th]
Original
1912
Earlier work this paper cites.
T. Zhou and A. Nahum, arXiv e-prints , arXiv:1912.12311 (2019b), arXiv:1912.12311 [cond-mat.str-el]
Original
1912
Earlier work this paper cites.
H.-J. Stöckmann, Quantum Chaos: An Introduction (Cambridge University Press, 1999)
1999
Earlier work this paper cites.
V. Balasubramanian and P. Kraus, Communications in Mathematical Physics 208
1999
Earlier work this paper cites.
P. Zanardi, Phys. Rev. A 63
2001
Earlier work this paper cites.
J. Kudler-Flam, Y. Kusuki, and S. Ryu, JHEP 04
Original
2001
Earlier work this paper cites.
S. de Haro, K. Skenderis, and S. N. Solodukhin, Communications in Mathematical Physics 217
2001
Earlier work this paper cites.
B. Collins, arXiv e-prints , math-ph/0205010 (2002), arXiv:math-ph/0205010 [math-ph]
2002
Earlier work this paper cites.
B. Bertini and L. Piroli, arXiv e-prints , arXiv:2004.13697 (2020), arXiv:2004.13697 [cond-mat.stat-mech]
Original
2004
Earlier work this paper cites.

Similar

P. Calabrese and J. Cardy, Journal of Statistical Mechanics: Theory and Experiment 2005
2005
Cited alongside, same era.
K. M. R. Audenaert and M. B. Plenio, New Journal of Physics 7
2005
Cited alongside, same era.
S. Ryu and T. Takayanagi, Journal of High Energy Physics 2006
2006
Cited alongside, same era.
V. Alba, arXiv e-prints , arXiv:2006.02788 (2020), arXiv:2006.02788 [cond-mat.stat-mech]
Original
2006
Cited alongside, same era.
T. Prosen and I. Pižorn, Phys. Rev. A 76
Original
2007
Cited alongside, same era.
V. E. Hubeny, M. Rangamani, and T. Takayanagi, Journal of High Energy Physics 2007