Entropic uncertainty relations for quantum information scrambling
Abstract
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.
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation; National Science Foundation (NSF)
- OSTI Identifier:
- 1619753
- Alternate Identifier(s):
- OSTI ID: 1597486
- Grant/Contract Number:
- SC0011632; PHY-1125565; PHY-1125915
- Resource Type:
- Published Article
- Journal Name:
- Communications Physics
- Additional Journal Information:
- Journal Name: Communications Physics Journal Volume: 2 Journal Issue: 1; Journal ID: ISSN 2399-3650
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- 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 Kingdom: 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 Kingdom. https://doi.org/10.1038/s42005-019-0179-8
Yunger Halpern, Nicole, Bartolotta, Anthony, and Pollack, Jason. Wed .
"Entropic uncertainty relations for quantum information scrambling". United Kingdom. https://doi.org/10.1038/s42005-019-0179-8.
@article{osti_1619753,
title = {Entropic uncertainty relations for quantum information scrambling},
author = {Yunger Halpern, Nicole and Bartolotta, Anthony and Pollack, Jason},
abstractNote = {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.},
doi = {10.1038/s42005-019-0179-8},
journal = {Communications Physics},
number = 1,
volume = 2,
place = {United Kingdom},
year = {2019},
month = {8}
}
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