Chaos in quantum channels

Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

doi:10.1007/JHEP02(2016)004

Title: Chaos in quantum channels

Abstract

For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

Authors:

Hosur, Pavan ^[1]; Qi, Xiao-Liang ^[1]; Roberts, Daniel A. ^[2]; Yoshida, Beni ^[3]

Stanford Univ., CA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); California Inst. of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Mon Feb 01 00:00:00 EST 2016

Research Org.:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1327290

Grant/Contract Number:: SC0012567

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AdS-CFT Correspondence; Holography and condensed matter physics (AdS/CMT); Gauge-gravity correspondence; Random Systems

Citation Formats


                    Hosur, Pavan, Qi, Xiao-Liang, Roberts, Daniel A., and Yoshida, Beni. Chaos in quantum channels.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP02(2016)004.

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                    Hosur, Pavan, Qi, Xiao-Liang, Roberts, Daniel A., & Yoshida, Beni. Chaos in quantum channels.  United States.  https://doi.org/10.1007/JHEP02(2016)004

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                    Hosur, Pavan, Qi, Xiao-Liang, Roberts, Daniel A., and Yoshida, Beni. Mon .  
"Chaos in quantum channels".  United States.  https://doi.org/10.1007/JHEP02(2016)004.  https://www.osti.gov/servlets/purl/1327290.

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@article{osti_1327290,

  title        = {Chaos in quantum channels},

  author       = {Hosur, Pavan and Qi, Xiao-Liang and Roberts, Daniel A. and Yoshida, Beni},

  abstractNote = {For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.},

  doi          = {10.1007/JHEP02(2016)004},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 2,

  volume       = 2016,

  place        = {United States},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

Copy to clipboard

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Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
text, January 2018

Sieberer, Lukas M.; Olsacher, Tobias; Elben, Andreas
arXiv
DOI: 10.48550/arxiv.1812.05876

Quantum Scrambling and State Dependence of the Butterfly Velocity
text, January 2018

Han, Xizhi; Hartnoll, Sean A.
arXiv
DOI: 10.48550/arxiv.1812.07598

Measurement-driven entanglement transition in hybrid quantum circuits
text, January 2019

Li, Yaodong; Chen, Xiao; Fisher, Matthew P. A.
arXiv
DOI: 10.48550/arxiv.1901.08092

Phases of scrambling in eigenstates
text, January 2019

Anous, Tarek; Sonner, Julian
arXiv
DOI: 10.48550/arxiv.1903.03143

Quantum information scrambling after a quantum quench
text, January 2019

Alba, Vincenzo; Calabrese, Pasquale
arXiv
DOI: 10.48550/arxiv.1903.09176

Anomalous Subdiffusion from Subsystem Symmetries
text, January 2019

Iaconis, Jason; Vijay, Sagar; Nandkishore, Rahul
arXiv
DOI: 10.48550/arxiv.1907.10629

Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
text, January 2019

Sünderhauf, Christoph; Piroli, Lorenzo; Qi, Xiao-Liang
arXiv
DOI: 10.48550/arxiv.1908.00775

Dynamics of quantum information
text, January 2019

Lewis-Swan, R. J.; Safavi-Naini, A.; Kaufman, A. M.
arXiv
DOI: 10.48550/arxiv.1908.11747

Conformal field theory and the web of quantum chaos diagnostics
text, January 2019

Kudler-Flam, Jonah; Nie, Laimei; Ryu, Shinsei
arXiv
DOI: 10.48550/arxiv.1910.14575

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Title: Chaos in quantum channels

Abstract

Citation Formats

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

Fast scramblers journal, October 2008

Towards the fast scrambling conjecture journal, April 2013

Average entropy of a subsystem journal, August 1993

Localized shocks journal, March 2015

Black holes and the butterfly effect journal, March 2014

Multiple shocks journal, December 2014

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

Stringy effects in scrambling journal, May 2015

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

Entanglement Tsunami: Universal Scaling in Holographic Thermalization journal, January 2014

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

Topological Entanglement Entropy journal, March 2006

Detecting Topological Order in a Ground State Wave Function journal, March 2006

Black holes: complementarity or firewalls? journal, February 2013

Better Late than Never: Information Retrieval from Black Holes journal, March 2013

An apologia for firewalls journal, September 2013

Eternal black holes in anti-de Sitter journal, April 2003

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

Bekenstein-Hawking Entropy and Strange Metals journal, November 2015

The finite group velocity of quantum spin systems journal, September 1972

Spectral Gap and Exponential Decay of Correlations journal, April 2006

Strong and Weak Thermalization of Infinite Nonintegrable Quantum Systems journal, February 2011

Entanglement Renormalization journal, November 2007

Bulk locality and quantum error correction in AdS/CFT journal, April 2015

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

Hot multiboundary wormholes from bipartite entanglement journal, October 2015

The typical-state paradox: diagnosing horizons with complexity: The typical-state paradox: diagnosing horizons with complexity journal, January 2016

The world as a hologram journal, November 1995

Entanglement is not enough: Entanglement is not enough journal, January 2016

A continuity property of the entropy density for spin lattice systems journal, December 1973

A sharp continuity estimate for the von Neumann entropy journal, June 2007

Quantum quenches in extended systems journal, June 2007

Holographic entanglement entropy from 2d CFT: heavy states and local quenches journal, February 2015

Holographic evolution of the mutual information journal, January 2012

Framework for classifying logical operators in stabilizer codes journal, May 2010

Black holes as mirrors: quantum information in random subsystems text, January 2007

Fast Scramblers text, January 2008

Framework for classifying logical operators in stabilizer codes text, January 2010

Towards the fast scrambling conjecture text, January 2011

Entanglement Tsunami: Universal Scaling in Holographic Thermalization text, January 2013

Ballistic spreading of entanglement in a diffusive nonintegrable system text, January 2013

Stringy effects in scrambling preprint, January 2014

Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet text, January 1992

Out-of-time-order correlations in many-body localized and thermal phases: Out-of-time-order correlations in many-body localized and thermal phases journal, December 2016

The Holographic Entropy Arrangement journal, February 2019

Conformal field theory and the web of quantum chaos diagnostics journal, January 2020

On the universality of late-time correlators in semi-classical 2d CFTs journal, August 2018

Holographic spacetimes as quantum circuits of path-integrations journal, December 2018

Barrier from chaos: operator entanglement dynamics of the reduced density matrix journal, December 2019

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

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model journal, April 2019

Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top journal, September 2019

Unscrambling the physics of out-of-time-order correlators journal, October 2018

Mimicking black hole event horizons in atomic and solid-state systems journal, November 2018

Verified quantum information scrambling journal, March 2019

Entropic uncertainty relations for quantum information scrambling journal, August 2019

Dynamics of quantum information journal, August 2019

Nuclear magnetic resonance for quantum computing: Techniques and recent achievements journal, February 2018

An SYK-like model without disorder journal, October 2019

Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity journal, July 2018

Optimizing measurement strengths for qubit quasiprobabilities behind out-of-time-ordered correlators journal, December 2019

Family of Sachdev-Ye-Kitaev models motivated by experimental considerations journal, June 2018

Entanglement features of random Hamiltonian dynamics journal, July 2018

Entangling power of time-evolution operators in integrable and nonintegrable many-body systems journal, November 2018

Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries journal, April 2019

Complexity growth rates for AdS black holes in massive gravity and f(R) gravity journal, December 2017

Accessing scrambling using matrix product operators journal, November 2019

Scrambling and thermalization in a diffusive quantum many-body system journal, June 2017

Approaching the chaotic regime with a fully connected superconducting quantum processor journal, December 2019

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices journal, January 2020

Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models journal, December 2019

Out-of-time-order correlation in marginal many-body localized systems journal, April 2017

Chaos and complexity in quantum mechanics journal, January 2020

Supersymmetric Sachdev-Ye-Kitaev models journal, January 2017

Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos journal, November 2018

Out‐of‐Time‐Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models journal, April 2020

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

Fast scramblers
journal, October 2008

Towards the fast scrambling conjecture
journal, April 2013

Average entropy of a subsystem
journal, August 1993

Localized shocks
journal, March 2015

Black holes and the butterfly effect
journal, March 2014

Multiple shocks
journal, December 2014

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

Stringy effects in scrambling
journal, May 2015

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

Entanglement Tsunami: Universal Scaling in Holographic Thermalization
journal, January 2014

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

Topological Entanglement Entropy
journal, March 2006

Detecting Topological Order in a Ground State Wave Function
journal, March 2006

Black holes: complementarity or firewalls?
journal, February 2013

Better Late than Never: Information Retrieval from Black Holes
journal, March 2013

An apologia for firewalls
journal, September 2013

Eternal black holes in anti-de Sitter
journal, April 2003

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

Bekenstein-Hawking Entropy and Strange Metals
journal, November 2015

The finite group velocity of quantum spin systems
journal, September 1972

Spectral Gap and Exponential Decay of Correlations
journal, April 2006

Strong and Weak Thermalization of Infinite Nonintegrable Quantum Systems
journal, February 2011

Entanglement Renormalization
journal, November 2007

Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

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

Hot multiboundary wormholes from bipartite entanglement
journal, October 2015

The typical-state paradox: diagnosing horizons with complexity: The typical-state paradox: diagnosing horizons with complexity
journal, January 2016

The world as a hologram
journal, November 1995

Entanglement is not enough: Entanglement is not enough
journal, January 2016

A continuity property of the entropy density for spin lattice systems
journal, December 1973

A sharp continuity estimate for the von Neumann entropy
journal, June 2007

Quantum quenches in extended systems
journal, June 2007

Holographic entanglement entropy from 2d CFT: heavy states and local quenches
journal, February 2015

Holographic evolution of the mutual information
journal, January 2012

Framework for classifying logical operators in stabilizer codes
journal, May 2010

Black holes as mirrors: quantum information in random subsystems
text, January 2007

Fast Scramblers
text, January 2008

Framework for classifying logical operators in stabilizer codes
text, January 2010

Towards the fast scrambling conjecture
text, January 2011

Entanglement Tsunami: Universal Scaling in Holographic Thermalization
text, January 2013

Ballistic spreading of entanglement in a diffusive nonintegrable system
text, January 2013

Stringy effects in scrambling
preprint, January 2014

Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
text, January 1992

Out-of-time-order correlations in many-body localized and thermal phases: Out-of-time-order correlations in many-body localized and thermal phases
journal, December 2016

The Holographic Entropy Arrangement
journal, February 2019

Conformal field theory and the web of quantum chaos diagnostics
journal, January 2020

On the universality of late-time correlators in semi-classical 2d CFTs
journal, August 2018

Holographic spacetimes as quantum circuits of path-integrations
journal, December 2018

Barrier from chaos: operator entanglement dynamics of the reduced density matrix
journal, December 2019

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

Unifying scrambling, thermalization and entanglement through measurement of fidelity out-of-time-order correlators in the Dicke model
journal, April 2019

Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top
journal, September 2019

Unscrambling the physics of out-of-time-order correlators
journal, October 2018

Mimicking black hole event horizons in atomic and solid-state systems
journal, November 2018

Verified quantum information scrambling
journal, March 2019

Entropic uncertainty relations for quantum information scrambling
journal, August 2019

Dynamics of quantum information
journal, August 2019

Nuclear magnetic resonance for quantum computing: Techniques and recent achievements
journal, February 2018

An SYK-like model without disorder
journal, October 2019

Eigenstate thermalization hypothesis, time operator, and extremely quick relaxation of fidelity
journal, July 2018

Optimizing measurement strengths for qubit quasiprobabilities behind out-of-time-ordered correlators
journal, December 2019

Family of Sachdev-Ye-Kitaev models motivated by experimental considerations
journal, June 2018

Entanglement features of random Hamiltonian dynamics
journal, July 2018

Entangling power of time-evolution operators in integrable and nonintegrable many-body systems
journal, November 2018

Random-matrix behavior of quantum nonintegrable many-body systems with Dyson's three symmetries
journal, April 2019

Complexity growth rates for AdS black holes in massive gravity and f(R) gravity
journal, December 2017

Accessing scrambling using matrix product operators
journal, November 2019

Scrambling and thermalization in a diffusive quantum many-body system
journal, June 2017

Approaching the chaotic regime with a fully connected superconducting quantum processor
journal, December 2019

Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
journal, January 2020

Tripartite information, scrambling, and the role of Hilbert space partitioning in quantum lattice models
journal, December 2019

Out-of-time-order correlation in marginal many-body localized systems
journal, April 2017

Chaos and complexity in quantum mechanics
journal, January 2020

Supersymmetric Sachdev-Ye-Kitaev models
journal, January 2017

Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
journal, November 2018

Out‐of‐Time‐Order Correlators and Quantum Phase Transitions in the Rabi and Dicke Models
journal, April 2020

Operator spreading in quantum maps
journal, March 2019

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

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath
journal, July 2017