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<p>Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive maps, which eliminates the need to identify eigenvalues of the output state. Notably, the Faddeev-LeVerrier algorithm establishes a relationship between the coefficients of characteristic polynomials and the moments of a matrix. This enables the existence of negative eigenvalues through the moments of the output state. The effectiveness of our criterion relies on the selection of positive maps, similar to the original positive maps criterion.</p>

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Entanglement certification from moments of positive maps

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Qing-Hua Zhang,
  • Xiaoyu Ma,
  • Shao-Ming Fei

摘要

Entanglement certification is crucial in physical experiments, particularly when only partial knowledge of the quantum state is available. In this context, we present an entanglement criterion based on positive but not completely positive maps, which eliminates the need to identify eigenvalues of the output state. Notably, the Faddeev-LeVerrier algorithm establishes a relationship between the coefficients of characteristic polynomials and the moments of a matrix. This enables the existence of negative eigenvalues through the moments of the output state. The effectiveness of our criterion relies on the selection of positive maps, similar to the original positive maps criterion.