Superdensity operators for spacetime quantum mechanics

Journal of High Energy Physics, Sep 2018

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.

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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 9 Downloads 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 Download to read the full article text Notes Open Access 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. References [1] V.I. Arnold, Mathematical methods of classical mechanics, Springer, Germany (1989).CrossRefGoogle Scholar [2] R. Haag, Local quantum physics: fields, particles, algebras, Springer, Germany (2012).zbMATHGoogle Scholar [3] R.B. Griffiths, Consistent histories and the interpretation of quantum mechanics, J. Statist. 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Jordan Cotler, Chao-Ming Jian, Xiao-Liang Qi, Frank Wilczek. Superdensity operators for spacetime quantum mechanics, Journal of High Energy Physics, 2018, 93, DOI: 10.1007/JHEP09(2018)093