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arXiv · 2201.07236

Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices

Zhiyuan Yao·Lei Pan·Shang Liu·Pengfei Zhang
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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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Zhiyuan Yao, Lei Pan, Shang Liu, Pengfei Zhang. 2022-01-18. Bounding Entanglement Entropy Using Zeros of Local Correlation Matrices. https://doi.org/10.1103/physrevresearch.4.l042037

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