DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Scrambling and complexity in phase space

; ; ;
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:  
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Name: Physical Review A Journal Volume: 99 Journal Issue: 6; Journal ID: ISSN 2469-9926
American Physical Society
Country of Publication:
United States

Citation Formats

Zhuang, Quntao, Schuster, Thomas, Yoshida, Beni, and Yao, Norman Y. Scrambling and complexity in phase space. United States: N. p., 2019. Web. doi:10.1103/PhysRevA.99.062334.
Zhuang, Quntao, Schuster, Thomas, Yoshida, Beni, & Yao, Norman Y. Scrambling and complexity in phase space. United States.
Zhuang, Quntao, Schuster, Thomas, Yoshida, Beni, and Yao, Norman Y. Tue . "Scrambling and complexity in phase space". United States.
title = {Scrambling and complexity in phase space},
author = {Zhuang, Quntao and Schuster, Thomas and Yoshida, Beni and Yao, Norman Y.},
abstractNote = {},
doi = {10.1103/PhysRevA.99.062334},
journal = {Physical Review A},
number = 6,
volume = 99,
place = {United States},
year = {2019},
month = {6}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

The Curious Nonexistence of Gaussian 2-Designs
journal, February 2014

  • Blume-Kohout, Robin; Turner, Peter S.
  • Communications in Mathematical Physics, Vol. 326, Issue 3
  • DOI: 10.1007/s00220-014-1894-3

Peres-Horodecki Separability Criterion for Continuous Variable Systems
journal, March 2000

Black holes as mirrors: quantum information in random subsystems
journal, September 2007

Gaussian quantum information
journal, May 2012

  • Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl
  • Reviews of Modern Physics, Vol. 84, Issue 2
  • DOI: 10.1103/RevModPhys.84.621

Multiqubit Clifford groups are unitary 3-designs
journal, December 2017

Towards the fast scrambling conjecture
journal, April 2013

  • Lashkari, Nima; Stanford, Douglas; Hastings, Matthew
  • Journal of High Energy Physics, Vol. 2013, Issue 4
  • DOI: 10.1007/JHEP04(2013)022

Out-of-time-ordered correlators in many-body localized systems: Out-of-time-ordered correlators in many-body localized systems
journal, December 2016

  • Huang, Yichen; Zhang, Yong-Liang; Chen, Xie
  • Annalen der Physik, Vol. 529, Issue 7
  • DOI: 10.1002/andp.201600318

Measuring the scrambling of quantum information
journal, October 2016

Convex resource theory of non-Gaussianity
journal, June 2018

Chaos and complexity by design
journal, April 2017

  • Roberts, Daniel A.; Yoshida, Beni
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)121

Quantum Computation over Continuous Variables
journal, February 1999

Ultimate classical communication rates of quantum optical channels
journal, September 2014

Quantum and Classical Lyapunov Exponents in Atom-Field Interaction Systems
journal, January 2019

  • Chávez-Carlos, Jorge; López-del-Carpio, B.; Bastarrachea-Magnani, Miguel A.
  • Physical Review Letters, Vol. 122, Issue 2
  • DOI: 10.1103/PhysRevLett.122.024101

Quantum thermalization and equilibrium state with multiple temperatures
journal, June 2014

Chaos in quantum channels
journal, February 2016

  • Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)004

Out-of-time-order correlation for many-body localization
journal, May 2017

Emergence of correlations in the process of thermalization of interacting bosons
journal, January 2019

Toward a Definition of Complexity for Quantum Field Theory States
journal, March 2018

Out-of-time-ordered correlators and purity in rational conformal field theories
journal, November 2016

  • Caputa, Paweł; Numasawa, Tokiro; Veliz-Osorio, Alvaro
  • Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 11
  • DOI: 10.1093/ptep/ptw157

The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
journal, May 2018

  • Kitaev, Alexei; Suh, S. Josephine
  • Journal of High Energy Physics, Vol. 2018, Issue 5
  • DOI: 10.1007/JHEP05(2018)183

Universal control of an oscillator with dispersive coupling to a qubit
journal, October 2015

Traversable wormholes via a double trace deformation
journal, December 2017

  • Gao, Ping; Jafferis, Daniel Louis; Wall, Aron C.
  • Journal of High Energy Physics, Vol. 2017, Issue 12
  • DOI: 10.1007/JHEP12(2017)151

Average entropy of a subsystem
journal, August 1993

Continuous-variable optical quantum-state tomography
journal, March 2009

Quantifying non-Gaussianity for quantum information
journal, November 2010

Chaos, complexity, and random matrices
journal, November 2017

  • Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu
  • Journal of High Energy Physics, Vol. 2017, Issue 11
  • DOI: 10.1007/JHEP11(2017)048

Holographic duality from random tensor networks
journal, November 2016

  • Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)009

Black holes and the butterfly effect
journal, March 2014

  • Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2014, Issue 3
  • DOI: 10.1007/JHEP03(2014)067

Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System
journal, September 2013

Fast scrambling on sparse graphs
journal, March 2019

  • Bentsen, Gregory; Gu, Yingfei; Lucas, Andrew
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 14
  • DOI: 10.1073/pnas.1811033116

Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
journal, May 2017

  • Gu, Yingfei; Qi, Xiao-Liang; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)125

Gapless spin-fluid ground state in a random quantum Heisenberg magnet
journal, May 1993

Fast scramblers
journal, October 2008

Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
journal, September 2018

Deterministically Encoding Quantum Information Using 100-Photon Schrodinger Cat States
journal, September 2013

Relative entropy is an exact measure of non-Gaussianity
journal, July 2013

Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System
journal, February 2017

Local Random Quantum Circuits are Approximate Polynomial-Designs
journal, August 2016

  • Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał
  • Communications in Mathematical Physics, Vol. 346, Issue 2
  • DOI: 10.1007/s00220-016-2706-8

Quantifying the non-Gaussian character of a quantum state by quantum relative entropy
journal, December 2008

Wave packet dynamics and chaos in the Hénon–Heiles system
journal, March 1984

  • Feit, M. D.; Fleck, J. A.
  • The Journal of Chemical Physics, Vol. 80, Issue 6
  • DOI: 10.1063/1.447051

Cross-Kerr Nonlinearity for Phonon Counting
journal, November 2017

Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet
journal, May 2017

  • Gärttner, Martin; Bohnet, Justin G.; Safavi-Naini, Arghavan
  • Nature Physics, Vol. 13, Issue 8
  • DOI: 10.1038/nphys4119

Direct dialling of Haar random unitary matrices
journal, March 2017

  • Russell, Nicholas J.; Chakhmakhchyan, Levon; O’Brien, Jeremy L.
  • New Journal of Physics, Vol. 19, Issue 3
  • DOI: 10.1088/1367-2630/aa60ed

Equilibration of quantum chaotic systems
journal, December 2013

Resource theory of non-Gaussian operations
journal, May 2018

Experimental observation of quantum chaos in a beam of light
journal, January 2012

  • Lemos, Gabriela B.; Gomes, Rafael M.; Walborn, Stephen P.
  • Nature Communications, Vol. 3, Issue 1
  • DOI: 10.1038/ncomms2214

Experimental realization of any discrete unitary operator
journal, July 1994

  • Reck, Michael; Zeilinger, Anton; Bernstein, Herbert J.
  • Physical Review Letters, Vol. 73, Issue 1
  • DOI: 10.1103/PhysRevLett.73.58

Black holes and random matrices
journal, May 2017

  • Cotler, Jordan S.; Gur-Ari, Guy; Hanada, Masanori
  • Journal of High Energy Physics, Vol. 2017, Issue 5
  • DOI: 10.1007/JHEP05(2017)118

Quantum chaos on a critical Fermi surface
journal, February 2017

  • Patel, Aavishkar A.; Sachdev, Subir
  • Proceedings of the National Academy of Sciences, Vol. 114, Issue 8
  • DOI: 10.1073/pnas.1618185114

Continuous Variable Quantum Cryptography Using Coherent States
journal, January 2002

Time evolution of entanglement entropy from black hole interiors
journal, May 2013

Optimal design for universal multiport interferometers
journal, January 2016

  • Clements, William R.; Humphreys, Peter C.; Metcalf, Benjamin J.
  • Optica, Vol. 3, Issue 12
  • DOI: 10.1364/OPTICA.3.001460

Solvable model for a dynamical quantum phase transition from fast to slow scrambling
journal, April 2017

Exploring Localization in Nuclear Spin Chains
journal, February 2018

Qubit-flip-induced cavity mode squeezing in the strong dispersive regime of the quantum Rabi model
journal, March 2017

  • Joshi, Chaitanya; Irish, Elinor K.; Spiller, Timothy P.
  • Scientific Reports, Vol. 7, Issue 1
  • DOI: 10.1038/srep45587

Information propagation in isolated quantum systems
journal, July 2017

Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
journal, December 2018

Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
journal, September 2015

A bound on chaos
journal, August 2016

  • Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas
  • Journal of High Energy Physics, Vol. 2016, Issue 8
  • DOI: 10.1007/JHEP08(2016)106

Disentangling Scrambling and Decoherence via Quantum Teleportation
journal, January 2019

Continuous variable teleportation as a generalized thermalizing quantum channel
journal, July 2002

  • Ban, Masashi; Sasaki, Masahide; Takeoka, Masahiro
  • Journal of Physics A: Mathematical and General, Vol. 35, Issue 28
  • DOI: 10.1088/0305-4470/35/28/102

Black holes: complementarity or firewalls?
journal, February 2013

  • Almheiri, Ahmed; Marolf, Donald; Polchinski, Joseph
  • Journal of High Energy Physics, Vol. 2013, Issue 2
  • DOI: 10.1007/JHEP02(2013)062

Operator Spreading and the Emergence of Dissipative Hydrodynamics under Unitary Evolution with Conservation Laws
journal, September 2018

Measuring Out-of-Time-Order Correlators on a Nuclear Magnetic Resonance Quantum Simulator
journal, July 2017

Verified quantum information scrambling
journal, March 2019

Unitary designs and codes
journal, April 2009

Exact and approximate unitary 2-designs and their application to fidelity estimation
journal, July 2009

Ordered Expansions in Boson Amplitude Operators
journal, January 1969

Quantum Entanglement Growth under Random Unitary Dynamics
journal, July 2017

Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation
journal, September 2018

  • Rakovszky, Tibor; Pollmann, Frank; von Keyserlingk, C. W.
  • Physical Review X, Vol. 8, Issue 3
  • DOI: 10.1103/PhysRevX.8.031058

Out-of-time-order correlators in quantum mechanics
journal, October 2017

  • Hashimoto, Koji; Murata, Keiju; Yoshii, Ryosuke
  • Journal of High Energy Physics, Vol. 2017, Issue 10
  • DOI: 10.1007/JHEP10(2017)138

Hudson’s theorem for finite-dimensional quantum systems
journal, December 2006

  • Gross, D.
  • Journal of Mathematical Physics, Vol. 47, Issue 12
  • DOI: 10.1063/1.2393152

Diving into traversable wormholes: Diving into traversable wormholes
journal, May 2017

  • Maldacena, Juan; Stanford, Douglas; Yang, Zhenbin
  • Fortschritte der Physik, Vol. 65, Issue 5
  • DOI: 10.1002/prop.201700034

Operator Spreading in Random Unitary Circuits
journal, April 2018

Operator Hydrodynamics, OTOCs, and Entanglement Growth in Systems without Conservation Laws
journal, April 2018

  • von Keyserlingk, C. W.; Rakovszky, Tibor; Pollmann, Frank
  • Physical Review X, Vol. 8, Issue 2
  • DOI: 10.1103/PhysRevX.8.021013

Evenly distributed unitaries: On the structure of unitary designs
journal, May 2007

  • Gross, D.; Audenaert, K.; Eisert, J.
  • Journal of Mathematical Physics, Vol. 48, Issue 5
  • DOI: 10.1063/1.2716992

Out-of-time-order operators and the butterfly effect
journal, September 2018

Decoupling with Random Quantum Circuits
journal, September 2015

Recovering Quantum Gates from Few Average Gate Fidelities
journal, October 2018

Localized shocks
journal, March 2015

  • Roberts, Daniel A.; Stanford, Douglas; Susskind, Leonard
  • Journal of High Energy Physics, Vol. 2015, Issue 3
  • DOI: 10.1007/JHEP03(2015)051

Cavity State Manipulation Using Photon-Number Selective Phase Gates
journal, September 2015

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

  • Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)149

Encoding a qubit in an oscillator
journal, June 2001

Random Quantum Circuits are Approximate 2-designs
journal, July 2009

Resource theory of quantum non-Gaussianity and Wigner negativity
journal, November 2018

The resource theory of stabilizer quantum computation
journal, January 2014