AI 中文总结
该研究表征含复X噪声的贝尔混合态的能力缺失区间与确定阈值，得到隐形传态、CJWR、CHSH及导引性等的相关区间与阈值，还给出不同噪声下的阈值规律。
AI 中文摘要
带噪声的贝尔混合态可携带纠缠、标准隐形传态可用性、投影测量 steerability（导引性）以及优化的Cavalcanti-Jones-Wiseman-Reid（CJWR）不等式和Clauser-Horne-Shimony-Holt（CHSH）不等式违背。若噪声已具备某种能力，当贝尔权重降低时，混合态可能在不同边界交叉处失去该能力后又恢复。我们表征了|Φ⁺⟩与任意两量子比特复X噪声混合态的能力缺失区间和确定阈值。泡利关联张量的闭式奇异值流给出了隐形传态无用、满足CJWR以及CHSH局域的精确区间，而正部分转置判据给出了可分态的精确区间。在固定布居数和相干幅度下，当噪声的Φ块相干性与贝尔相干性之间的相对相位从0增至π时，这些区间会变宽。确定阈值形成一条通用链，从纠缠经隐形传态可用性和三设置CJWR见证到常见两设置CJWR见证和CHSH非局域阈值。将隐形传态可用性替换为导引性则得到第二条链，尽管它们的阈值互不有序。对于任意纯两量子比特噪声，投影测量和任意正算子值测度的双向导引性阈值等于纠缠阈值。对于任意乘积噪声，有效X态奇异值流给出隐形传态可用性、CJWR见证和CHSH非局域阈值。若局域噪声因子为纯态，则纠缠阈值和所有四个导引性阈值均为零。对于一般满秩混合X噪声，有限设置半定规划给出未知定向投影测量导引性阈值的上界。
英文摘要
Noisy Bell mixtures may carry entanglement, standard teleportation usefulness, projective-measurement steerability, and optimized Cavalcanti-Jones-Wiseman-Reid (CJWR) and Clauser-Horne-Shimony-Holt (CHSH) violations. If the noise already has an ability, the mixture may lose and later recover it at distinct boundary crossings as the Bell weight decreases. We characterize ability-absence intervals and definitive thresholds for mixtures of $|Φ^+\rangle$ with arbitrary complex two-qubit $X$ noise. A closed-form singular-value flow of the Pauli correlation tensor gives the exact teleportation-useless, CJWR-satisfying, and CHSH-local intervals, while the positive partial transpose criterion gives the exact separable interval. At fixed populations and coherence magnitudes, these intervals widen as the relative phase between the $Φ$-block coherence of the noise and the Bell coherence increases from $0$ to $π$. The definitive thresholds form a universal chain from entanglement through teleportation usefulness and the three-setting CJWR witness to the common two-setting CJWR witness and CHSH-nonlocal threshold. Replacing teleportation usefulness by steerability gives a second chain, although their thresholds are not mutually ordered. For arbitrary pure two-qubit noise, the steerability thresholds in both directions for projective measurements and arbitrary positive operator-valued measures equal the entanglement threshold. For arbitrary product noise, an effective $X$-state singular-value flow gives the teleportation usefulness, CJWR witness, and CHSH-nonlocal thresholds. If a local noise factor is pure, the entanglement threshold and all four steerability thresholds are zero. For generic full-rank mixed $X$ noise, finite-setting semidefinite programs give upper bounds on the unknown directional projective-measurement steerability thresholds.
