Entanglement in quantum field theory via wavelet representations

Daniel J. George, Yuval R. Sanders, Mohsen Bagherimehrab, Barry C. Sanders, and Gavin K. Brennen
Phys. Rev. D 106, 036025 – Published 26 August 2022

Abstract

Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of free scalar bosonic and Ising model fermionic QFTs using wavelets. Making use of the orthogonality and self-similarity of the wavelet basis functions, we demonstrate some well-known relations such as scale-dependent subsystem entanglement entropy and renormalization of correlations in the ground state. We also find some new applications of the wavelet transform as a compressed representation of ground states of QFTs which can be used to illustrate quantum phase transitions via fidelity overlap and holographic entanglement of purification.

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  • Received 11 May 2022
  • Accepted 29 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.036025

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Daniel J. George1,2,3,*, Yuval R. Sanders1,3,4, Mohsen Bagherimehrab5,6,7, Barry C. Sanders5, and Gavin K. Brennen1,3

  • 1Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia
  • 2Sydney Quantum Academy, Sydney, NSW 2000, Australia
  • 3ARC Centre of Excellence in Engineered Quantum Systems, Macquarie University, Sydney, NSW 2109, Australia
  • 4Centre for Quantum Software and Information, University of Technology Sydney, Sydney, NSW 2007, Australia
  • 5Institute for Quantum Science and Technology, University of Calgary, Calgary, Alberta T2N 1N4, Canada
  • 6Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5G 1Z8, Canada
  • 7Department of Computer Science, University of Toronto, Toronto, Ontario M5S 2E4, Canada

  • *Corresponding author. dan.george@hdr.mq.edu.au

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Issue

Vol. 106, Iss. 3 — 1 August 2022

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