Entropic uncertainty relations for quantum information scrambling

Journal Article · 06 August 2019 · Communications Physics

DOI: https://doi.org/10.1038/s42005-019-0179-8 · OSTI ID:1619753

Yunger Halpern, Nicole ; Bartolotta, Anthony; Pollack, Jason

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.

• Research Organization: California Inst. of Technology (CalTech), Pasadena, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); Natural Sciences and Engineering Research Council of Canada; Simons Foundation; USDOE; USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: SC0011632
• OSTI ID: 1619753
• Journal Information: Communications Physics, Journal Name: Communications Physics Journal Issue: 1 Vol. 2; ISSN 2399-3650
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United Kingdom
• Language: English