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August 16, 2026Open Access

Tensor Product Structure and Non-associative Entanglement Degree非结合代数的张量积结构与非结合纠缠度

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Authors

ZLZhongqiang Liu

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Overview

Algebraic analysis reveals associator operator bounds in three-dimensional dissipative algebra, highlighting an intrinsic non-associative entanglement metric.

Key Points

  • To analyze the associator operator structure on the two-body state space of the three-dimensional dissipative algebra (TDDA) and develop an intrinsic algebraic entanglement metric.
  • Derived analytical decomposition and direction-locking theorems governing associator operators on two-body pure and single-body tensors.
  • Performed symbolic computation and large-scale random-matrix sampling experiments to test algebraic identities and evaluate dimensional limits.
  • Established a maximum associator operator rank of 7 for generic entangled two-body states within an 8-dimensional constraint shell, which degenerates to 6 or 5 under collinear distributions.
  • Demonstrated that single-body associators are confined to a fixed 1D ray defined by the intermediate element, with magnitude set by the non-classical projection plane area determinant.
  • Defined a discrete non-associative entanglement degree taking values in {0, 1, 2} based on the discovered rank hierarchy.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817ab4f2fb91fc834aece0https://doi.org/10.5281/zenodo.21952787
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