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<p>Revealing and quantifying entanglement of particles is central for understanding the foundations of quantum mechanics and its implications for modern technology. Recent works have demonstrated entanglement of free electrons and photons; however, the quantum properties of multiple free electrons, and the extent of their entanglement, remain largely unexplored. Here we investigate the degree of coherence and entanglement in a free-space electron beam in an ultrafast electron microscope. We introduce a two-electron quantum walk that transforms the quantum state into different bases for quantum state tomography of entangled or partially entangled electron–electron pairs. The method can distinguish point-like particles from delocalized two-electron matter waves with or without classical correlations or entanglement. As a first application, we study multiparticle quantum effects in short pulses of hundreds of electrons under strong Coulomb correlations. Pairs of postselected electrons are delocalized matter waves with correlation between different parts of the two-electron state. The degree of entanglement is less than 7% due to a limited purity of the initial states and decoherence effects from unmeasured reservoir electrons. This measurement tool provides the necessary means to create and measure entangled free electrons for exploring fundamental quantum physics and advancing quantum electron microscopy.</p>

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Two-electron quantum walks for probing entanglement and decoherence in an electron microscope

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • Offek Tziperman,
  • David Nabben,
  • Ron Ruimy,
  • Jacob Holder,
  • Ethan Nussinson,
  • Yiqi Fang,
  • Alexey Gorlach,
  • Daniel Kazenwadel,
  • Aviv Karnieli,
  • Ido Kaminer,
  • Peter Baum

摘要

Revealing and quantifying entanglement of particles is central for understanding the foundations of quantum mechanics and its implications for modern technology. Recent works have demonstrated entanglement of free electrons and photons; however, the quantum properties of multiple free electrons, and the extent of their entanglement, remain largely unexplored. Here we investigate the degree of coherence and entanglement in a free-space electron beam in an ultrafast electron microscope. We introduce a two-electron quantum walk that transforms the quantum state into different bases for quantum state tomography of entangled or partially entangled electron–electron pairs. The method can distinguish point-like particles from delocalized two-electron matter waves with or without classical correlations or entanglement. As a first application, we study multiparticle quantum effects in short pulses of hundreds of electrons under strong Coulomb correlations. Pairs of postselected electrons are delocalized matter waves with correlation between different parts of the two-electron state. The degree of entanglement is less than 7% due to a limited purity of the initial states and decoherence effects from unmeasured reservoir electrons. This measurement tool provides the necessary means to create and measure entangled free electrons for exploring fundamental quantum physics and advancing quantum electron microscopy.