发表机构
Reichman University; Tel-Hai University of Kiryat Shmona in the Galilee; MIGAL—Galilee Research Institute（莱希曼大学; 加利利基里亚特谢莫纳泰尔海大学; MIGAL-加利利研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了多体系统中与MABK贝尔分数兼容的最小GHZ可提取性，给出了精确界并证明其最优性，同时分类了达到该界的态并建立了稳定性估计。
AI 中文摘要
我们确定了对于任意大于二方的参与方数量，与Mermin-Ardehali-Belinskii-Klyshko（MABK）贝尔分数相容的最小Greenberger-Horne-Zeilinger（GHZ）可提取性。可提取性是指通过独立的局域量子信道所能获得的与GHZ态的最大平方重叠。在双可分离界和量子最大值之间，精确最小值是从二分之一到一的仿射插值。该界对任意局域维度的张量积上的正规态以及任意二元测量都成立。我们通过一个从四方开始统一的解析证明，解决了先前未解决的六方或更多方的情况。我们还确定了当每个局域系统为量子比特时的精确最小值，并证明在每一个内部分数处，该值严格高于无限制界。一个qutrit和其余所有方的量子比特，在分数变化时通过固定测量达到该界的每一个点。对于至少四方且分数为严格内部值的情况，我们分类了所有达到该界且局域支持维度乘积最小的态。对于至少四方、一方为qutrit其余为量子比特的情况，我们还证明了当超过仿射最小值的可提取性余量较小时，达到该混合态的迹范数距离（在局域幺正变换下）以该余量的平方根的常数倍为界。指数$1/2$是最优的，且这些常数在归一化分数的每个固定内部区间上独立于参与方数量。
英文摘要
We determine the least Greenberger-Horne-Zeilinger (GHZ) extractability compatible with a Mermin-Ardehali-Belinskii-Klyshko (MABK) Bell score for every number of parties greater than two. Extractability is the largest squared overlap with a GHZ state obtainable by separate local quantum channels. Between the biseparable bound and the quantum maximum, the exact minimum is the affine interpolation from one half to one. The bound holds for normal states on tensor products of arbitrary local dimension and arbitrary binary measurements. We settle the previously unresolved range of six or more parties with an analytic proof that is uniform from four parties onward. We also determine the exact minimum when every local system is a qubit, and show that it lies strictly above the unrestricted bound at every interior score. One qutrit and qubits at all remaining parties attain every point of the bound with measurements fixed as the score varies. For at least four parties and strict interior scores, we classify all states attaining the bound with the minimum product of local support dimensions. For at least four parties on one qutrit and qubits elsewhere, we also prove that, when the extractability excess above the affine minimum is small, the trace-norm distance from the attaining mixture, up to local unitaries, is bounded by a constant times the square root of that excess. The exponent $1/2$ is optimal, and the constants are independent of the number of parties on every fixed interior interval of normalized scores.
Comments35 pages, 1 figure
