发表机构
Nankai University; North China Electric Power University; Tianjin Normal University（南开大学; 华北电力大学; 天津师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究解析了n量子比特广义GHZ态对EMABK不等式的最大量子违背，提出关联张量方法，构造两种测量策略饱和上界，证明纠缠广义GHZ态在EMABK不等式下存在严格量子-经典分离。
AI 中文摘要
我们解析表征了n量子比特广义Greenberger-Horne-Zeilinger（GHZ）态对扩展Mermin-Ardehali-Belinskii-Klyshko（EMABK）族不等式的最大量子违背。我们提出了一种关联张量方法，其中贝尔值被表示为量子关联张量与有效系数张量的弗罗贝尼乌斯内积。有效系数张量的秩约束结合冯·诺依曼迹不等式，得到由重塑关联张量的两个最大奇异值决定的上界。对于广义GHZ态，我们确定了完整的奇异谱并得到分段解析上界。随后，我们构造了两种互补的测量策略，它们在整个参数范围内使EMABK的上界达到饱和：第一种是纯MABK策略，其中所有测量方向都位于布洛赫球的赤道平面内；第二种是混合策略，它递归地将低阶MABK反对角算子与全σ_z张量积相结合。所得的分段解析表达式在最大纠缠极限下恢复了标准MABK Tsirelson界2^((n-1)/2)，并在乘积态极限下趋近于经典局域隐变量界。它进一步表明，每个纠缠的广义GHZ态在EMABK不等式下都表现出严格的量子-经典分离，从而消除了标准MABK不等式在部分纠缠区域的非违背区域。
英文摘要
We analytically characterize the maximal quantum violation of the extended Mermin-Ardehali-Belinskii-Klyshko (EMABK) family of inequalities by $n$-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states. We develop a correlation-tensor approach in which the Bell value is expressed as the Frobenius inner product of the quantum correlation tensor and an effective coefficient tensor. A rank constraint on the latter, together with the von Neumann trace inequality, yields an upper bound governed by the two largest singular values of the reshaped correlation-tensor. For generalized GHZ states, we determine the complete singular spectrum and obtain a piecewise analytic upper bound. We then construct two complementary measurement strategies that saturate the bound for EMABK throughout the entire parameter range. The first is a purely MABK strategy in which all measurement directions lie in the equatorial plane of the Bloch sphere. The second is a hybrid strategy that recursively combines lower-order MABK anti-diagonal operators with the fully-$σ_z$ tensor product. The resulting piecewise analytic expression recovers the standard MABK Tsirelson bound $2^{(n-1)/2}$ in the maximally entangled limit and approaches the classical local-hidden-variable bound in the product-state limits. It further shows that every entangled generalized GHZ state exhibits a strict quantum-classical separation under the EMABK inequality, thereby eliminating the nonviolation region of the standard MABK inequality in the partially entangled regime.
Comments18 pages, 3 figures
