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

Title: Entropic uncertainty relations for quantum information scrambling

Journal Article · · Communications Physics
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

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.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation; National Science Foundation (NSF); USDOE
Grant/Contract Number:
SC0011632; PHY-1125565; PHY-1125915
OSTI ID:
1619753
Alternate ID(s):
OSTI ID: 1597486
Journal Information:
Communications Physics, Vol. 2, Issue 1; ISSN 2399-3650
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 18 works
Citation information provided by
Web of Science

References (80)

Unscrambling the physics of out-of-time-order correlators journal October 2018
Generalized entropic uncertainty relations journal March 1988
The Spectrum in the Sachdev-Ye-Kitaev Model text January 2016
Towards the fast scrambling conjecture journal April 2013
Measuring the scrambling of quantum information journal October 2016
Chaos and complexity by design journal April 2017
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
�ber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik journal March 1927
Weak values as interference phenomena journal March 2015
The spectrum in the Sachdev-Ye-Kitaev model journal April 2016
Black holes and the butterfly effect journal March 2014
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
Gapless spin-fluid ground state in a random quantum Heisenberg magnet journal May 1993
Classification of out-of-time-order correlators text January 2017
Fast scramblers journal October 2008
Exploring Localization in Nuclear Spin Chains text January 2016
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
Products of weak values: Uncertainty relations, complementarity, and incompatibility journal May 2016
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet text January 2016
Direct measurement of the Kirkwood-Rihaczek distribution for the spatial properties of a coherent light beam journal June 2010
Reversing quantum trajectories with analog feedback text January 2013
Compressive Direct Measurement of the Quantum Wave Function text January 2014
Measuring out-of-time-order correlations and multiple quantum spectra in a trapped-ion quantum magnet journal May 2017
Reversing Quantum Trajectories with Analog Feedback journal February 2014
The Uncertainty Principle journal June 1931
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
The uncertainty principle journal November 2010
Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories journal August 2016
Experimental test of entropic noise-disturbance uncertainty relations for spin-1/2 measurements text January 2015
Matrix Analysis book November 1996
Experimental Realization of Sequential Weak Measurements of Arbitrary Non-commuting Pauli Observables text January 2018
Exploring Localization in Nuclear Spin Chains journal February 2018
Entropic uncertainty and measurement reversibility text January 2015
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
Matrix analysis text January 1965
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
Out-of-time-order fluctuation-dissipation theorem text January 2016
Chaos in quantum channels text January 2015
A bound on chaos journal August 2016
Observation of non-classical correlations in sequential measurements of photon polarization journal October 2016
Jarzynski-like equality for the out-of-time-ordered correlator text January 2016
Zur Quantenmechanik einfacher Bewegungstypen journal April 1927
Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet text January 1992
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 text January 2018
A Framework for Non-Asymptotic Quantum Information Theory preprint January 2012
Measurement of many-body chaos using a quantum clock text January 2016
Direct Measurement of the Quantum Wavefunction text January 2011
A bound on chaos text January 2015
Chaos and complexity by design text January 2016
Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling journal February 2019
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
Formulation of the uncertainty relations in terms of the Renyi entropies text January 2006
Introduction to Weak Measurements and Weak Values journal May 2013
Direct measurement of the quantum wavefunction journal June 2011
Towards the fast scrambling conjecture text January 2011
Fast Scramblers text January 2008
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
Strong unitary and overlap uncertainty relations: theory and experiment text January 2017
Relative entropies and their use in quantum information theory preprint January 2016
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
Direct Measurement of Kirkwood-Rihaczek distribution for spatial properties of coherent light beam text January 2009

Cited By (5)