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<p>The stability of entanglement across scaling regimes is a fundamental challenge in quantum science, critically influencing the prospects of quantum technologies and our understanding of macroscopic quantum phenomena. This work investigates a fundamental entanglement dichotomy between finite and infinite scales in generalized Greenberger–Horne–Zeilinger (GGHZ) states. We demonstrate that the entanglement of finite-sized GGHZ qudit states is size-independent, a feature verified by computing two complementary entanglement measures. In stark contrast, we rigorously prove the complete decoherence of the associated infinite-volume state under the thermodynamic limit. By bridging techniques from quantum information with operator algebras, our results establish a critical constraint on the stability of macroscopic entanglement, with direct implications for quantum science.</p>

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Infinite-scale decoherence of GGHZ-states: an algebraic approach

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Abdessatar Souissi,
  • Amenallah Andolsi

摘要

The stability of entanglement across scaling regimes is a fundamental challenge in quantum science, critically influencing the prospects of quantum technologies and our understanding of macroscopic quantum phenomena. This work investigates a fundamental entanglement dichotomy between finite and infinite scales in generalized Greenberger–Horne–Zeilinger (GGHZ) states. We demonstrate that the entanglement of finite-sized GGHZ qudit states is size-independent, a feature verified by computing two complementary entanglement measures. In stark contrast, we rigorously prove the complete decoherence of the associated infinite-volume state under the thermodynamic limit. By bridging techniques from quantum information with operator algebras, our results establish a critical constraint on the stability of macroscopic entanglement, with direct implications for quantum science.