三 qutrit 中最小基数的真正不可扩展乘积基
A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits
AI总结：
研究解决了真正不可扩展乘积基是否存在的开放问题，构造出三 qutrit 的最小基数 14 的 GUPB，扩展了构造并给出其在量子纠缠与非局域性中的应用。
AI中文摘要：
真正不可扩展乘积基（GUPB）是否存在一直是一个开放问题，我们在 GUPB 存在的最小三部分希尔伯特空间中，构造了一个基数为 14 的明确三 qutrit GUPB，结合不存在基数小于 14 的三 qutrit GUPB 的结论，证明 14 是最小基数。填充程序进一步将该构造扩展到所有局域维度至少为 3 的三部分系统。作为应用，三 qutrit GUPB 的 13 维正交补上的归一化投影算子在部分转置下为正，且在所有二分划分下均存在有界纠缠，同时该 GUPB 表现出无纠缠的强量子非局域性。
英文摘要：
It has remained an open question whether a genuinely unextendible product basis (GUPB) exists. We resolve this problem by constructing an explicit three-qutrit GUPB of cardinality fourteen in the smallest tripartite Hilbert space in which a GUPB can exist. Together with the nonexistence of three-qutrit GUPBs of cardinality less than fourteen, our construction proves that fourteen is the minimum cardinality. A padding procedure further extends the construction to all tripartite systems whose local dimensions are at least three. As applications, the normalized projector onto the thirteen-dimensional orthogonal complement of the three-qutrit GUPB is positive under partial transposition and bound entangled across every bipartition, while the GUPB exhibits strong quantum nonlocality without entanglement.
