#### Superdensity operators for spacetime quantum mechanics

Journal of High Energy Physics
September 2018, 2018:93 | Cite as
Superdensity operators for spacetime quantum mechanics
AuthorsAuthors and affiliations
Jordan CotlerChao-Ming JianXiao-Liang QiFrank Wilczek
Open Access
Regular Article - Theoretical Physics
First Online: 17 September 2018
Received: 14 July 2018
Accepted: 24 August 2018
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Abstract
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac’s transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a super-density operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. We also suggest experimental protocols for measuring spacetime entropies.
Keywords Space-Time Symmetries Lattice Quantum Field Theory
ArXiv ePrint: 1711.03119
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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
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© The Author(s) 2018
Authors and Affiliations
Jordan Cotler1Email authorChao-Ming Jian23Xiao-Liang Qi14Frank Wilczek56781.Stanford Institute for Theoretical PhysicsStanford UniversityStanfordU.S.A.2.Station Q, Microsoft ResearchSanta BarbaraU.S.A.3.Kavli Institute of Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A.4.Institute for Advanced StudyPrincetonU.S.A.5.Center for Theoretical PhysicsMITCambridgeU.S.A.6.The Oskar Klein Centre for Cosmoparticle PhysicsStockholm University, AlbanovaStockholmSweden7.T. D. Lee Institute and Wilczek Quantum CenterShanghai Jiao Tong UniversityShanghaiChina8.Department of Physics and Origins ProjectArizona State UniversityTempeU.S.A.