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  • Letter
  • Open Access

Bounding entanglement entropy using zeros of local correlation matrices

Zhiyuan Yao1, Lei Pan1, Shang Liu2,*, and Pengfei Zhang3,†

  • 1Institute for Advanced Study, Tsinghua University, Beijing 100084, China
  • 2Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA
  • 3Institute for Quantum Information and Matter and Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA

  • *sliu.phys@gmail.com
  • †PengfeiZhang.physics@gmail.com
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Phys. Rev. Research 4, L042037 – Published 28 November, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L042037

Abstract

Correlation functions and entanglement are two different aspects to characterize quantum many-body states. While many correlation functions are experimentally accessible, entanglement entropy (EE), the simplest characterization of quantum entanglement, is usually difficult to measure. In this Letter, we propose a protocol to bound EE by local measurements. This protocol utilizes local correlation matrices and focuses on their (approximate) zero eigenvalues. Given a quantum state, each (approximate) zero eigenvalue can be used to define a set of local projection operators. An auxiliary Hamiltonian can then be constructed by summing these projectors. When the construction only involves projectors of zero eigenvalues, we prove the EE of a subsystem is bounded by the ground-state degeneracy of the auxiliary Hamiltonian on this subsystem. When projectors from nonzero eigenvalues are included, we show the EE can be bounded by a thermal entropy of the subsystem. Our protocol can be applied experimentally to investigate exotic quantum many-body states prepared in quantum simulators.

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Outline

Information

Phys. Rev. Research 4, L042037– Published 28 November, 2022
  • Received 1 February 2022
  • Revised 6 May 2022
  • Accepted 9 November 2022
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