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Multipartite Entanglement in Stabilizer Tensor Networks

Nezami, Sepehr and Walter, Michael (2020) Multipartite Entanglement in Stabilizer Tensor Networks. Physical Review Letters, 125 (24). Art. No. 241602. ISSN 0031-9007. doi:10.1103/physrevlett.125.241602.

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Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge for general quantum systems. In this work, we initiate the study of multipartite entanglement in a rich, yet tractable class of quantum states called stabilizer tensor networks. We demonstrate that, for generic stabilizer tensor networks, the geometry of the tensor network informs the multipartite entanglement structure of the state. In particular, we show that the average number of Greenberger-Horne-Zeilinger (GHZ) triples that can be extracted from a stabilizer tensor network is small, implying that tripartite entanglement is scarce. This, in turn, restricts the higher-partite entanglement structure of the states. Recent research in quantum gravity found that stabilizer tensor networks reproduce important structural features of the AdS / CFT correspondence, including the Ryu-Takayanagi formula for the entanglement entropy and certain quantum error correction properties. Our results imply a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks, as well as a novel formula for the third moment of random stabilizer states, which we expect to find further applications in quantum information.

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Additional Information:© 2020 American Physical Society. (Received 21 September 2020; accepted 11 November 2020; published 10 December 2020) It is a pleasure to thank David Gross, Patrick Hayden, Debbie Leung, Xiao-Liang Qi, Lenny Susskind, Zhao Yang, and Huangjun Zhu for inspiring discussions. S. N. acknowledges support from a Stanford Graduate Fellowship. M. W. gratefully acknowledges support from FQXI, the Simons Foundation, the DoD Multidisciplinary University Research Initiative (MURI), and an NWO Veni grant (No. 680-47-459).
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Foundational Questions Institute (FQXI)UNSPECIFIED
Simons FoundationUNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)680-47-459
Stanford UniversityUNSPECIFIED
Department of DefenseUNSPECIFIED
Issue or Number:24
Record Number:CaltechAUTHORS:20201215-141036428
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107090
Deposited By: George Porter
Deposited On:16 Dec 2020 15:05
Last Modified:16 Nov 2021 18:59

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