• Open Access

Connector Tensor Networks: A Renormalization-Type Approach to Quantum Certification

Miguel Navascués, Sukhbinder Singh, and Antonio Acín
Phys. Rev. X 10, 021064 – Published 19 June 2020

Abstract

As quantum technologies develop, we acquire control of an ever-growing number of quantum systems. Unfortunately, current tools to detect relevant quantum properties of quantum states, such as entanglement and Bell nonlocality, suffer from severe scalability issues and can be computed only for systems of a very modest size of around six sites. In order to address large many-body systems, we propose a renormalization-type approach based on a class of local linear transformations called connectors, which can be used to coarse grain the system in a way that preserves the property under investigation. Repeated coarse graining produces a system of manageable size, whose properties can then be explored by means of the usual techniques for small systems. In the case of a successful detection of the desired property, the method outputs a linear witness which admits an exact tensor network representation composed of connectors. We demonstrate the power of our method by certifying entanglement, Bell nonlocality, and supraquantum Bell nonlocality in systems with hundreds of sites using a normal desktop computer.

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  • Received 5 August 2019
  • Revised 6 March 2020
  • Accepted 15 April 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021064

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.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Miguel Navascués1, Sukhbinder Singh2, and Antonio Acín3,4

  • 1Institute for Quantum Optics and Quantum Information (IQOQI) Vienna Austrian Academy of Sciences, Vienna 1090., Austria
  • 2Max-Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam 14476, Germany
  • 3ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
  • 4ICREA-Institucio Catalana de Recerca i Estudis Avançats, Lluis Companys 23, 08010 Barcelona, Spain

Popular Summary

Certain quantum features with no classical counterpart, such as entanglement and the violation of Bell inequalities, arise as collective properties of systems with several components and cannot be detected by looking at the individual parts. Recognizing whether a given system exhibits such features is central in the study of quantum fundamentals and quantum information science but is generally a very complicated problem, often even intractable. In our work, we propose a novel method to detect quantum properties. While existing methods can address systems with just a few components, our approach is scalable and can be applied to systems with hundreds of parts.

Our approach exploits an important insight from statistical physics: A large system can often be coarse grained to a smaller one in ways that leave important global properties intact while discarding small-scale details. We develop new classes of coarse-graining transformations, called connectors, which preserve the feature of interest. The net result of these transformations is to map the original problem of detecting quantum properties to a simpler one with a tractable number of components.

While we showcase our method by constructing specific classes of connectors for detecting entanglement and Bell nonlocality, the formalism is remarkably general: It can be applied to identify collective global properties in any system’s network. We therefore expect that connector theory will find application in other areas of quantum theory.

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Vol. 10, Iss. 2 — April - June 2020

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