Camargo, Hugo A. and Hackl, Lucas and Heller, Michal P. and Jahn, Alexander and Windt, Bennet (2021) Long Distance Entanglement of Purification and Reflected Entropy in Conformal Field Theory. Physical Review Letters, 127 (14). Art. No. 141604. ISSN 0031-9007. doi:10.1103/PhysRevLett.127.141604. https://resolver.caltech.edu/CaltechAUTHORS:20211014-212143934
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Abstract
Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both the entanglement of purification and reflected entropy is enhanced with respect to the mutual information behavior by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest.
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| Alternate Title: | Long-distance entanglement of purification in conformal field theory | ||||||||||||||||
| Additional Information: | © 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. (Received 17 March 2021; revised 28 June 2021; accepted 23 August 2021; published 29 September 2021) We would like to thank J. Eisert and T. Takayanagi for collaborations on related subjects and M. C. Bañuls, T. Faulkner, J. Knaute, C. Pattison, D. Radicevic, L. Shaposhnik, S. Singh, V. Svensson, B. Swingle, and L. Tagliacozzo for useful discussions and comments on the draft. Our special thanks go to P. Bueno who in response to the first version of the manuscript pointed out to us that the behavior encapsulated by (7) was also seen in the reflected entropy in free fermion and free boson QFTs [56,57]. The Gravity, Quantum Fields and Information group at the Max Planck Institute for Gravitational Physics (Albert Einstein Institute) is supported by the Alexander von Humboldt Foundation and the Federal Ministry for Education and Research through the Sofja Kovalevskaja Award. A. J. is supported by the FQXi. H. C. is partially supported by the Konrad-Adenauer-Stiftung through their Sponsorship Program for Foreign Students and by the International Max Planck Research School for Mathematical and Physical Aspects of Gravitation, Cosmology and Quantum Field Theory. | ||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||
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| Issue or Number: | 14 | ||||||||||||||||
| DOI: | 10.1103/PhysRevLett.127.141604 | ||||||||||||||||
| Record Number: | CaltechAUTHORS:20211014-212143934 | ||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211014-212143934 | ||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||
| ID Code: | 111451 | ||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||
| Deposited By: | George Porter | ||||||||||||||||
| Deposited On: | 18 Oct 2021 22:11 | ||||||||||||||||
| Last Modified: | 18 Oct 2021 22:11 |
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