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Title: Entropic uncertainty relations for quantum information scrambling

Abstract

Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called “scrambling,” is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields’ notions of quantum-operation disagreement.

Authors:
ORCiD logo [1];  [2];  [3]
  1. Harvard-Smithsonian Inst. for Theoretical Atomic Molecular and Optical Physics (ITAMP), Cambridge, MA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States). Inst. for Quantum Information and Matter; Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
  3. Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation; National Science Foundation (NSF)
OSTI Identifier:
1597486
Grant/Contract Number:  
[SC0011632; PHY-1125565; PHY-1125915]
Resource Type:
Accepted Manuscript
Journal Name:
Communications Physics
Additional Journal Information:
[ Journal Volume: 2; Journal Issue: 1]; Journal ID: ISSN 2399-3650
Publisher:
Springer Nature
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Yunger Halpern, Nicole, Bartolotta, Anthony, and Pollack, Jason. Entropic uncertainty relations for quantum information scrambling. United States: N. p., 2019. Web. doi:10.1038/s42005-019-0179-8.
Yunger Halpern, Nicole, Bartolotta, Anthony, & Pollack, Jason. Entropic uncertainty relations for quantum information scrambling. United States. doi:10.1038/s42005-019-0179-8.
Yunger Halpern, Nicole, Bartolotta, Anthony, and Pollack, Jason. Wed . "Entropic uncertainty relations for quantum information scrambling". United States. doi:10.1038/s42005-019-0179-8. https://www.osti.gov/servlets/purl/1597486.
@article{osti_1597486,
title = {Entropic uncertainty relations for quantum information scrambling},
author = {Yunger Halpern, Nicole and Bartolotta, Anthony and Pollack, Jason},
abstractNote = {Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called “scrambling,” is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields’ notions of quantum-operation disagreement.},
doi = {10.1038/s42005-019-0179-8},
journal = {Communications Physics},
number = [1],
volume = [2],
place = {United States},
year = {2019},
month = {8}
}

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Works referenced in this record:

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


Generalized entropic uncertainty relations
journal, March 1988


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

Measuring the scrambling of quantum information
journal, October 2016


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

Strong Unitary and Overlap Uncertainty Relations: Theory and Experiment
journal, June 2018


Realization of a measurement of a ‘‘weak value’’
journal, March 1991


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

�ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik
journal, March 1927


Fine Grained Chaos in AdS 2 Gravity
journal, March 2018


Weak values as interference phenomena
journal, March 2015


The spectrum in the Sachdev-Ye-Kitaev model
journal, April 2016

  • Polchinski, Joseph; Rosenhaus, Vladimir
  • Journal of High Energy Physics, Vol. 2016, Issue 4
  • DOI: 10.1007/JHEP04(2016)001

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

Partial-Measurement Backaction and Nonclassical Weak Values in a Superconducting Circuit
journal, August 2013


Experimental realization of sequential weak measurements of non-commuting Pauli observables
journal, January 2019

  • Chen, Jiang-Shan; Hu, Meng-Jun; Hu, Xiao-Min
  • Optics Express, Vol. 27, Issue 5
  • DOI: 10.1364/OE.27.006089

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


Fast scramblers
journal, October 2008


Jarzynski-like equality for the out-of-time-ordered correlator
journal, January 2017


Direct Measurement of the Density Matrix of a Quantum System
journal, September 2016


Compressive Direct Measurement of the Quantum Wave Function
journal, August 2014

  • Mirhosseini, Mohammad; Magaña-Loaiza, Omar S.; Hashemi Rafsanjani, Seyed Mohammad
  • Physical Review Letters, Vol. 113, Issue 9
  • DOI: 10.1103/PhysRevLett.113.090402

Products of weak values: Uncertainty relations, complementarity, and incompatibility
journal, May 2016


Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam
journal, June 2010


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

Reversing Quantum Trajectories with Analog Feedback
journal, February 2014


Measurement of many-body chaos using a quantum clock
journal, December 2016


Entropic uncertainty relations and their applications
journal, February 2017


Procedure for Direct Measurement of General Quantum States Using Weak Measurement
journal, February 2012


Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories
journal, August 2016


Exploring Localization in Nuclear Spin Chains
journal, February 2018


Experimental test of uncertainty relations for general unitary operators
journal, January 2017


Resilience of scrambling measurements
journal, June 2018


Strengthening weak measurements of qubit out-of-time-order correlators
journal, July 2018

  • Dressel, Justin; González Alonso, José Raúl; Waegell, Mordecai
  • Physical Review A, Vol. 98, Issue 1
  • DOI: 10.1103/PhysRevA.98.012132

Quasiprobability behind the out-of-time-ordered correlator
journal, April 2018


Formulation of the uncertainty relations in terms of the Rényi entropies
journal, November 2006


Entropic uncertainty and measurement reversibility
journal, July 2016


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

Observation of non-classical correlations in sequential measurements of photon polarization
journal, October 2016


Classification of out-of-time-order correlators
journal, January 2019


Zur Quantenmechanik einfacher Bewegungstypen
journal, April 1927


Remarks on the Sachdev-Ye-Kitaev model
journal, November 2016


Significance of the imaginary part of the weak value
journal, January 2012


The Uncertainty Principle
journal, July 1929


Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
journal, February 2019

  • González Alonso, José Raúl; Yunger Halpern, Nicole; Dressel, Justin
  • Physical Review Letters, Vol. 122, Issue 4
  • DOI: 10.1103/PhysRevLett.122.040404

How the result of a measurement of a component of the spin of a spin- 1/2 particle can turn out to be 100
journal, April 1988


Introduction to Weak Measurements and Weak Values
journal, May 2013


Direct measurement of the quantum wavefunction
journal, June 2011

  • Lundeen, Jeff S.; Sutherland, Brandon; Patel, Aabid
  • Nature, Vol. 474, Issue 7350
  • DOI: 10.1038/nature10120

Measuring Incompatible Observables by Exploiting Sequential Weak Values
journal, October 2016


Uncertainty in Quantum Measurements
journal, February 1983


Out-of-time-order fluctuation-dissipation theorem
journal, January 2018


Experimental investigation of quantum entropic uncertainty relations for multiple measurements in pure diamond
journal, May 2017


Experimental Test of Entropic Noise-Disturbance Uncertainty Relations for Spin- 1 / 2 Measurements
journal, July 2015


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


Observing Dirac’s Classical Phase Space Analog to the Quantum State
journal, February 2014