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Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are "as random as a coin-toss".
1909
Earlier work this paper cites.
1909
Earlier work this paper cites.
Pascual Jordan, “Über kanonische transformationen in der quantenmechanik. ii,” Zeitschrift für Physik
1926
Earlier work this paper cites.
Paul Adrien Maurice Dirac, “On the analogy between classical and quantum mechanics,” Reviews of Modern Physics
1945
Earlier work this paper cites.
SM Ulam and J von Neumann, “On combination of stochastic and deterministic processes. preliminary report,” Bull. Amer. Math. Soe
1947
Earlier work this paper cites.
ECG Sudarshan, PM Mathews, and Jayaseetha Rau, “Stochastic dynamics of quantum-mechanical systems,” Physical Review
1961
Earlier work this paper cites.
VI Arnold and A Avez,
1968
Earlier work this paper cites.
Tien-Yien Li and James A. Yorke, “Period three implies chaos,”
1975
Earlier work this paper cites.
Robert M May, “Simple mathematical models with very complicated dynamics,” Nature
1976
Earlier work this paper cites.
Mitchell J Feigenbaum, “Quantitative universality for a class of nonlinear transformations,” Journal of statistical physics
1978
Earlier work this paper cites.
Michael V Berry, Nandor L Balazs, Michael Tabor, and André Voros, “Quantum maps,” Annals of Physics
1979
Earlier work this paper cites.
JH Hannay and Michael V Berry, “Quantization of linear maps on a torus-fresnel diffraction by a periodic grating,” Physica D: Nonlinear Phenomena
1980
Earlier work this paper cites.
Clinton J Oxenrider and Richard D Hill, “On the matrix reorderings
1985
Earlier work this paper cites.
NL Balazs and A Voros, “The quantized baker’s transformation,” EPL (Europhysics Letters)
1987
Earlier work this paper cites.
Nandor L Balazs and André Voros, “The quantized baker’s transformation,” Annals of Physics
1989
Earlier work this paper cites.
M Saraceno, “Classical structures in the quantized baker transformation,”
1990
Earlier work this paper cites.
“Chaos and quantum physics: Les houches, session LII,” (Elsevier Science Publishers BV, 1991)
1991
Earlier work this paper cites.
JP Keating, “The cat maps: quantum mechanics and classical motion,” Nonlinearity
1991
Earlier work this paper cites.
A.M. Ozorio de Almeida and M. Saraceno, “Periodic orbit theory for the quantized baker’s map,”
1991
Earlier work this paper cites.
Joseph Ford, Giorgio Mantica, and Gerald H Ristow, “The arnol’d cat: Failure of the correspondence principle,” Physica D: Nonlinear Phenomena
1991
Earlier work this paper cites.
P.W. O’Connor, S. Tomsovic, and E.J. Heller, “Accuracy of semiclassical dynamics in the presence of chaos,”
1992
Earlier work this paper cites.
Freeman J Dyson and Harold Falk, “Period of a discrete cat mapping,” The American Mathematical Monthly
1992
Earlier work this paper cites.
Alan Edelman, Eric Kostlan, and Michael Shub, “How many eigenvalues of a random matrix are real?” Journal of the American Mathematical Society
1994
Earlier work this paper cites.
Marcos Saraceno and André Voros, “Towards a semiclassical theory of the quantum baker’s map,” Physica D: Nonlinear Phenomena
1994
Earlier work this paper cites.
Asher Peres, “Separability criterion for density matrices,” Physical Review Letters
1996
Earlier work this paper cites.
Paolo Zanardi, Christof Zalka, and Lara Faoro, “Entangling power of quantum evolutions,” Phys. Rev. A
2000
Earlier work this paper cites.
A. Higuchi and A. Sudbery, “How entangled can two couples get?”
2000
Earlier work this paper cites.
Fumio Hiai and Dénes Petz,
2000
Earlier work this paper cites.
Rüdiger Schack and Carlton M Caves, “Shifts on a finite qubit string: A class of quantum baker’s maps,” Applicable Algebra in Engineering, Communication and Computing
2000
Earlier work this paper cites.
Alejandro MF Rivas, M Saraceno, and AM Ozorio De Almeida, “Quantization of multidimensional cat maps,” Nonlinearity
2000
Earlier work this paper cites.
Paolo Zanardi, “Entanglement of quantum evolutions,”
2001
Earlier work this paper cites.
2001
Earlier work this paper cites.
N. Khaneja, R. Brockett, and S. J. Glaser, “Time optimal control in spin systems,” Phys. Rev
2001
Cited alongside, same era.
B. Kraus and J. I. Cirac, “Optimal creation of entanglement using a two-qubit gate,” Phys. Rev
2001
Cited alongside, same era.
Yaakov S Weinstein, MA Pravia, EM Fortunato, Seth Lloyd, and David G Cory, “Implementation of the quantum fourier transform,” Physical review letters
2001
Cited alongside, same era.
Edward Ott,
2002
Cited alongside, same era.
Kai Chen and Ling-An Wu, “A matrix realignment method for recognizing entanglement,” arXiv preprint quant-ph/0205017 (2002)
2002
Cited alongside, same era.
Herbert Goldstein, Charles Poole, and John Safko,
2002
Cited alongside, same era.
Pavan Hosur, Xiao-Liang Qi, Daniel A. Roberts, and Beni Yoshida, “Chaos in quantum channels,”
2016
Later among the works it cites.
Marek Smaczyński, Wojciech Roga, and Karol Życzkowski, “Selfcomplementary quantum channels,” Open Systems & Information Dynamics
2016
Later among the works it cites.
Boris Gutkin and Vladimir Osipov, “Classical foundations of many-particle quantum chaos,” Nonlinearity
2016
Later among the works it cites.
Adam Nahum, Jonathan Ruhman, Sagar Vijay, and Jeongwan Haah, “Quantum entanglement growth under random unitary dynamics,” Physical Review X
2017
Later among the works it cites.
Bhargavi Jonnadula, Prabha Mandayam, Karol Życzkowski, and Arul Lakshminarayan, “Impact of local dynamics on entangling power,” Physical Review A
2017
Later among the works it cites.
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Esposti M D and Graffi S,
2003
Cited alongside, same era.
Jon Tyson, “Operator-schmidt decomposition of the quantum fourier transform on n1 n2,”
2003
Cited alongside, same era.
Oliver Rudolph, “Some properties of the computable cross-norm criterion for separability,” Physical Review A
2003
Cited alongside, same era.
Karol Zyczkowski, Marek Kus, Wojciech Słomczyński, and Hans-Jürgen Sommers, “Random unistochastic matrices,” Journal of Physics A: Mathematical and General
2003
Cited alongside, same era.
Jun Zhang, Jiri Vala, Shankar Sastry, and K. Birgitta Whaley, “Geometric theory of nonlocal two-qubit operations,”
2003
Cited alongside, same era.
F Faure and S Nonnenmacher, “On the maximal scarring for quantum cat map eigenstates,” Commun. Math. Phys
2004
Cited alongside, same era.
Z. Puchala and J.A. Miszczak, “Symbolic integration with respect to the haar measure on the unitary groups,”
2017
Later among the works it cites.
Adam Nahum, Sagar Vijay, and Jeongwan Haah, “Operator spreading in random unitary circuits,”
2018
Later among the works it cites.
Vedika Khemani, Ashvin Vishwanath, and David A Huse, “Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws,” Physical Review X
2018
Later among the works it cites.
CW Von Keyserlingk, Tibor Rakovszky, Frank Pollmann, and Shivaji Lal Sondhi, “Operator hydrodynamics, otocs, and entanglement growth in systems without conservation laws,” Physical Review X
2018
Later among the works it cites.
Amos Chan, Andrea De Luca, and JT Chalker, “Solution of a minimal model for many-body quantum chaos,” Physical Review X
2018
Later among the works it cites.
Bruno Bertini, Pavel Kos, and T. Prosen, “Exact spectral form factor in a minimal model of many-body quantum chaos,”
2018
Later among the works it cites.
Rajarshi Pal and Arul Lakshminarayan, “Entangling power of time-evolution operators in integrable and nonintegrable many-body systems,”
2018
Later among the works it cites.
Felix Huber, Christopher Eltschka, Jens Siewert, and Otfried Gühne, “Bounds on absolutely maximally entangled states from shadow inequalities, and the quantum macwilliams identity,” Journal of Physics A: Mathematical and Theoretical
2018
Later among the works it cites.
Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell,
2019
Later among the works it cites.
Sarang Gopalakrishnan and Austen Lamacraft, “Unitary circuits of finite depth and infinite width from quantum channels,”
2019
Later among the works it cites.
Giorgio Mantica, “Many-body systems and quantum chaos: The multiparticle quantum arnol’d cat,” Condensed Matter
2019
Later among the works it cites.
Petr Braun, Daniel Waltner, Maram Akila, Boris Gutkin, and Thomas Guhr, “Transition from quantum chaos to localization in spin chains,”
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
2020
Later among the works it cites.
Lorenzo Piroli, Bruno Bertini, J Ignacio Cirac, and Tomaž Prosen, “Exact dynamics in dual-unitary quantum circuits,” Physical Review B
2020
Later among the works it cites.
2020
Later among the works it cites.
Roman Frigg, Joseph Berkovitz, and Fred Kronz, “The Ergodic Hierarchy,” in
2020
Later among the works it cites.
Suhail Ahmad Rather, S. Aravinda, and Arul Lakshminarayan, “Creating ensembles of dual unitary and maximally entangling quantum evolutions,”
2020
Later among the works it cites.
Bhargavi Jonnadula, Prabha Mandayam, Karol Życzkowski, and Arul Lakshminarayan, “Entanglement measures of bipartite quantum gates and their thermalization under arbitrary interaction strength,”
2020
Later among the works it cites.
Ravi Prakash and Arul Lakshminarayan, “Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the ehrenfest timescale,”
2020
Later among the works it cites.
Bin Yan, Lukasz Cincio, and Wojciech H. Zurek, “Information scrambling and loschmidt echo,”
2020
Later among the works it cites.
2021
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2021
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Suhail Ahmad Rather, Aravinda S, and Arul Lakshminarayan, (2021), in preparation
2021
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Adam Burchardt, Private communication (2021)
2021
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