发表机构
Scuola Normale Superiore（意大利高等师范学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对PPT信道下的纠缠蒸馏，推导了PPT可蒸馏纠缠的正则化公式与两种单字母逆定理，证明其可严格小于正则化Rains界，还给出了基于纠缠负性的可靠下界，解决了相关开放问题。
AI 中文摘要
我们在量子香农理论框架下，研究部分转置共轭下保持完全正定性的操作（即PPT信道）下的纠缠蒸馏，该框架中误差渐近趋于零但非零。主要结果包括：(a) 基于类测量相对熵量的PPT可蒸馏纠缠的正则化公式；(b) 两种不同的单字母逆定理，一种基于算子二次型，另一种基于Hirschman对哈达玛三线定理的强化。作为(b)的直接应用，我们证明PPT可蒸馏纠缠可严格小于正则化Rains界，从而解决了纠缠操控理论中的一个开放问题[Regula等人，NJP 21:103017，2019]。该差距已在3×3 Werner态中显现：在反对称权重25/26处，经认证的上界为0.62107 ebits，小于（正则化）Rains界，后者等于25/26 log₂5 - log₂3 ≈ 0.64766 ebits。此外，(a)还隐含了基于纠缠负性的PPT可蒸馏纠缠的可靠下界，这为定性已知的“任何NPT态均可PPT蒸馏”[Eggeling等人，PRL 87:257902，2001]提供了定量对应。
英文摘要
We study entanglement distillation under operations that remain completely positive under partial-transpose conjugation, a.k.a. PPT channels, in the standard quantum Shannon theory regime of asymptotically vanishing but non-zero error. Our main results are: (a) a regularised formula for the PPT distillable entanglement in terms of a measured-relative-entropy-like quantity; and (b) two different single-letter converses, one based on operator quadratic forms and the other on Hirschman's strengthening of the Hadamard three-line theorem. As an immediate application of (b), we show that the PPT distillable entanglement can be strictly smaller than the regularised Rains bound, thereby resolving an open problem in the theory of entanglement manipulation [Regula et al., NJP 21:103017, 2019]. A gap appears already for $3\times 3$ Werner states: at antisymmetric weight $25/26$, a certified upper bound of $0.62107$ ebits lies below the (regularised) Rains bound, which equals $\frac{25}{26} \log_2 5 - \log_2 3 \approx 0.64766$ ebits. On a different note, (a) implies a faithful lower bound on the PPT distillable entanglement in terms of the entanglement negativity, which provides a quantitative counterpart to the qualitatively known fact that any NPT state is PPT distillable [Eggeling et al., PRL 87:257902, 2001].
Comments31+7 pages, 1 figure
