On non-genuinely entangled quantum states by a regularized alternative minimization method

Abstract Non-genuine quantum entanglement determination remains challenging in multipartite systems due to structural complexity. We develop a tensor-based framework with simplex and L 2 norm constraints, and propose a Regularized Alternating Minimization algorithm with convergence guarantees, which is extendable to multipartite systems. An accelerated Truncated Singular Value Decomposition-inspired heuristic enhances computational efficiency for large-scale approximations. Numerical experiments on noisy GHZ and W states demonstrate extended separability boundaries and validation of our methodology. This work bridges quantum theory with computational optimization, offering new tools for the determination of non-genuine quantum entanglement.