Built on

T. Rakovszky, F. Pollmann, and C. W. von Keyserlingk, “Sub-ballistic Growth of Rényi Entropies due to Diffusion,” Phys. Rev. Lett
Original
1901
Earlier work this paper cites.
N. Hunter-Jones, “Unitary designs from statistical mechanics in random quantum circuits,” arXiv:1905.12053 [quant-ph]
Original
1905
Earlier work this paper cites.
P. Reimann, “Transportless equilibration in isolated many-body quantum systems,” New J. Phys
Original
1905
Earlier work this paper cites.
Á. M. Alhambra, J. Riddell, and L. P. García-Pintos, “Time evolution of correlation functions in quantum many-body systems,” Phys. Rev. Lett
Original
1906
Earlier work this paper cites.
T. Rakovszky, C. W. von Keyserlingk, and F. Pollmann, “Entanglement growth after inhomogenous quenches,” Phys. Rev. B
Original
1907
Earlier work this paper cites.
D. Faiez, D. Šafránek, J. Deutsch, and A. Aguirre, “Typical and extreme entropies of long-lived isolated quantum systems,” Phys. Rev. A
Original
1908
Earlier work this paper cites.
Á. M. Alhambra, A. Anshu, and H. Wilming, “Revivals imply quantum many-body scars,” Phys. Rev. B
Original
1911
Earlier work this paper cites.
J. Cotler and N. Hunter-Jones, “Spectral decoupling in many-body quantum chaos,” arXiv:1911.02026 [hep-th]
Original
1911
Earlier work this paper cites.
F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill, “Models of quantum complexity growth,” arXiv:1912.04297 [hep-th]
Original
1912
Earlier work this paper cites.
A. W. Harrow and R. A. Low, “Random Quantum Circuits are Approximate 2-designs,” Commun. Math. Phys
Original
1919
Earlier work this paper cites.
P. Bocchieri and A. Loinger, “Quantum Recurrence Theorem,” Phys. Rev
1957
Earlier work this paper cites.
L. S. Schulman, “Note on the quantum recurrence theorem,” Phys. Rev. A
1978
Earlier work this paper cites.
M. E. Fisher, “Walks, walls, wetting, and melting,” J. Stat. Phys
1984
Earlier work this paper cites.
D. A. Huse and M. E. Fisher, “Commensurate melting, domain walls, and dislocations,” Phys. Rev. B
1984
Earlier work this paper cites.
D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett
1993
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E
1994
Earlier work this paper cites.
L. Dyson, M. Kleban, and L. Susskind, “Disturbing implications of a cosmological constant,” JHEP
2002
Earlier work this paper cites.
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth, “Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-Clifford gates,” arXiv:2002.09524 [quant-ph]
Original
2002
Earlier work this paper cites.
B. Bertini and L. Piroli, “Scrambling in Random Unitary Circuits: Exact Results,” Phys. Rev. B
Original
2004
Earlier work this paper cites.
S. Popescu, A. J. Short, and A. Winter, “Entanglement and the foundations of statistical mechanics,” Nat. Phys
2006
Earlier work this paper cites.
P. Hayden, D. W. Leung, and A. Winter, “Aspects of Generic Entanglement,” Commun. Math. Phys
2006
Earlier work this paper cites.
S. Dooley and G. Kells, “Enhancing the effect of quantum many-body scars on dynamics by minimising the effective dimension,” arXiv:2006.03099 [quant-ph]
Original
2006
Earlier work this paper cites.
L. V. Delacretaz, “Heavy Operators and Hydrodynamic Tails,” SciPost Phys
Original
2006
Earlier work this paper cites.
A. D. Linde, “Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem,” JCAP
2007
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP
Original
2007
Earlier work this paper cites.

Similar

R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio, “Generic Entanglement Can Be Generated Efficiently,” Phys. Rev. Lett
2007
Cited alongside, same era.
D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs,” J. Math. Phys
2007
Cited alongside, same era.
P. Reimann, “Foundation of Statistical Mechanics under Experimentally Realistic Conditions,” Phys. Rev. Lett
Original
2008
Cited alongside, same era.
R. Bousso, B. Freivogel, and I.-S. Yang, “Boltzmann babies in the proper time measure,” Phys. Rev. D
Original
2008
Cited alongside, same era.
D. N. Page, “Return of the Boltzmann Brains,” Phys. Rev. D
2008
Cited alongside, same era.

Then

F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki, “Local Random Quantum Circuits are Approximate Polynomial-Designs,” Commun. Math. Phys
Original
2016
Later among the works it cites.
P. Reimann, “Typical fast thermalization processes in closed many-body systems,” Nat. Comm
Original
2016
Later among the works it cites.
A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science
2016
Later among the works it cites.
C. Gogolin and J. Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Reports on Progress in Physics
Original
2016
Later among the works it cites.

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2020

Fluctuations of subsystem entropies at late times

Cotler, Jordan, Hunter-Jones, Nicholas, Ranard, Daniel

Understand

We study the fluctuations of subsystem entropies in closed quantum many-body systems after thermalization.

Using a combination of analytics and numerics for both random quantum circuits and Hamiltonian dynamics, we find that the statistics of such entropy fluctuations is drastically different than in the classical setting.
For instance, shortly after a system thermalizes, the probability of entropy fluctuations for a subregion is suppressed in the dimension of the Hilbert space of the complementary subregion.
This suppression becomes increasingly stringent as a function of time, ultimately depending on the exponential of the Hilbert space dimension, until extremely late times when the amount of suppression saturates.

Built on

T. Rakovszky, F. Pollmann, and C. W. von Keyserlingk, “Sub-ballistic Growth of Rényi Entropies due to Diffusion,” Phys. Rev. Lett
Original
1901
Earlier work this paper cites.
N. Hunter-Jones, “Unitary designs from statistical mechanics in random quantum circuits,” arXiv:1905.12053 [quant-ph]
Original
1905
Earlier work this paper cites.
P. Reimann, “Transportless equilibration in isolated many-body quantum systems,” New J. Phys
Original
1905
Earlier work this paper cites.
Á. M. Alhambra, J. Riddell, and L. P. García-Pintos, “Time evolution of correlation functions in quantum many-body systems,” Phys. Rev. Lett
Original
1906
Earlier work this paper cites.
T. Rakovszky, C. W. von Keyserlingk, and F. Pollmann, “Entanglement growth after inhomogenous quenches,” Phys. Rev. B
Original
1907
Earlier work this paper cites.
D. Faiez, D. Šafránek, J. Deutsch, and A. Aguirre, “Typical and extreme entropies of long-lived isolated quantum systems,” Phys. Rev. A
Original
1908
Earlier work this paper cites.
Á. M. Alhambra, A. Anshu, and H. Wilming, “Revivals imply quantum many-body scars,” Phys. Rev. B
Original
1911
Earlier work this paper cites.
J. Cotler and N. Hunter-Jones, “Spectral decoupling in many-body quantum chaos,” arXiv:1911.02026 [hep-th]
Original
1911
Earlier work this paper cites.
F. G. S. L. Brandão, W. Chemissany, N. Hunter-Jones, R. Kueng, and J. Preskill, “Models of quantum complexity growth,” arXiv:1912.04297 [hep-th]
Original
1912
Earlier work this paper cites.
A. W. Harrow and R. A. Low, “Random Quantum Circuits are Approximate 2-designs,” Commun. Math. Phys
Original
1919
Earlier work this paper cites.
P. Bocchieri and A. Loinger, “Quantum Recurrence Theorem,” Phys. Rev
1957
Earlier work this paper cites.
L. S. Schulman, “Note on the quantum recurrence theorem,” Phys. Rev. A
1978
Earlier work this paper cites.
M. E. Fisher, “Walks, walls, wetting, and melting,” J. Stat. Phys
1984
Earlier work this paper cites.
D. A. Huse and M. E. Fisher, “Commensurate melting, domain walls, and dislocations,” Phys. Rev. B
1984
Earlier work this paper cites.
D. N. Page, “Average entropy of a subsystem,” Phys. Rev. Lett
1993
Earlier work this paper cites.
M. Srednicki, “Chaos and quantum thermalization,” Phys. Rev. E
1994
Earlier work this paper cites.
L. Dyson, M. Kleban, and L. Susskind, “Disturbing implications of a cosmological constant,” JHEP
2002
Earlier work this paper cites.
J. Haferkamp, F. Montealegre-Mora, M. Heinrich, J. Eisert, D. Gross, and I. Roth, “Quantum homeopathy works: Efficient unitary designs with a system-size independent number of non-Clifford gates,” arXiv:2002.09524 [quant-ph]
Original
2002
Earlier work this paper cites.
B. Bertini and L. Piroli, “Scrambling in Random Unitary Circuits: Exact Results,” Phys. Rev. B
Original
2004
Earlier work this paper cites.
S. Popescu, A. J. Short, and A. Winter, “Entanglement and the foundations of statistical mechanics,” Nat. Phys
2006
Earlier work this paper cites.
P. Hayden, D. W. Leung, and A. Winter, “Aspects of Generic Entanglement,” Commun. Math. Phys
2006
Earlier work this paper cites.
S. Dooley and G. Kells, “Enhancing the effect of quantum many-body scars on dynamics by minimising the effective dimension,” arXiv:2006.03099 [quant-ph]
Original
2006
Earlier work this paper cites.
L. V. Delacretaz, “Heavy Operators and Hydrodynamic Tails,” SciPost Phys
Original
2006
Earlier work this paper cites.
A. D. Linde, “Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem,” JCAP
2007
Earlier work this paper cites.
P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP
Original
2007
Earlier work this paper cites.

Similar

R. Oliveira, O. C. O. Dahlsten, and M. B. Plenio, “Generic Entanglement Can Be Generated Efficiently,” Phys. Rev. Lett
2007
Cited alongside, same era.
D. Gross, K. Audenaert, and J. Eisert, “Evenly distributed unitaries: On the structure of unitary designs,” J. Math. Phys
2007
Cited alongside, same era.
P. Reimann, “Foundation of Statistical Mechanics under Experimentally Realistic Conditions,” Phys. Rev. Lett
Original
2008
Cited alongside, same era.
R. Bousso, B. Freivogel, and I.-S. Yang, “Boltzmann babies in the proper time measure,” Phys. Rev. D
Original
2008
Cited alongside, same era.
D. N. Page, “Return of the Boltzmann Brains,” Phys. Rev. D
2008
Cited alongside, same era.

Then

F. G. S. L. Brandão, A. W. Harrow, and M. Horodecki, “Local Random Quantum Circuits are Approximate Polynomial-Designs,” Commun. Math. Phys
Original
2016
Later among the works it cites.
P. Reimann, “Typical fast thermalization processes in closed many-body systems,” Nat. Comm
Original
2016
Later among the works it cites.
A. M. Kaufman, M. E. Tai, A. Lukin, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, “Quantum thermalization through entanglement in an isolated many-body system,” Science
2016
Later among the works it cites.
C. Gogolin and J. Eisert, “Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems,” Reports on Progress in Physics
Original
2016
Later among the works it cites.

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

A. Rolandi and H. Wilming, “Extensive Rényi entropies in matrix product states,” arXiv:2008.11764 [quant-ph]

Original

2008

Cited alongside, same era.

N. Linden, S. Popescu, A. J. Short, and A. Winter, “Quantum mechanical evolution towards thermal equilibrium,” Phys. Rev. E

Original

2009

Cited alongside, same era.

C. Dankert, R. Cleve, J. Emerson, and E. Livine, “Exact and approximate unitary 2-designs and their application to fidelity estimation,” Phys. Rev. A

2009

Cited alongside, same era.

R. A. Low, “Large deviation bounds for k k -designs,” Proc. R. Soc. A

Original

2009

Cited alongside, same era.

A. De Simone, A. H. Guth, A. D. Linde, M. Noorbala, M. P. Salem, and A. Vilenkin, “Boltzmann brains and the scale-factor cutoff measure of the multiverse,” Phys. Rev. D

Original

2010

Cited alongside, same era.

N. Linden, S. Popescu, A. J. Short, and A. Winter, “On the speed of fluctuations around thermodynamic equilibrium,” New J. Phys

Original

2010

Cited alongside, same era.

M. C. Bañuls, J. I. Cirac, and M. B. Hastings, “Strong and weak thermalization of infinite nonintegrable quantum systems,” Phys. Rev. Lett

Original

2011

Cited alongside, same era.

H. Labuhn, D. Barredo, S. Ravets, S. De Léséleuc, T. Macrì, T. Lahaye, and A. Browaeys, “Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models,” Nature

2016

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

Original

2017

Later among the works it cites.

T. Farrelly, F. G. S. L. Brandão, and M. Cramer, “Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems,” Phys. Rev. Lett

Original

2017

Later among the works it cites.

L. P. García-Pintos, N. Linden, A. S. L. Malabarba, A. J. Short, and A. Winter, “Equilibration time scales of physically relevant observables,” Phys. Rev. X

Original