标题： 有限高斯辅助协议和用于最大化类空真空纠缠的圆锥度量 显示英文标题

标题： Finite Gaussian assistance protocols and a conic metric for extremizing spacelike vacuum entanglement

摘要： 在纯高斯三部分划分中，两个参与者（$AB$）之间的纠缠范围可以通过在第三个（$C$）内执行的高斯测量的经典通信进行纯化。首先，本工作引入了一种直接方法来计算用于去除任何（$AB$）高斯噪声的一系列投影（$C$）测量，从而避免了先前协议中的发散问题。接下来，开发了一个多模态圆锥框架，以追求可能在（$AB$）之间揭示或需要的最大（高斯辅助纠缠，GEOA）或最小（高斯纠缠形成，GEOF）纯纠缠。在此框架内，出现了一个几何必要且充分的纠缠条件，即双重封闭的圆锥体积，定义了圆锥优化的新距离度量。对于无质量及有质量自由标量场中的类空真空纠缠，极化此距离得到（1）GEOA的最高已知下界，这是第一个随着真空分离增加而保持渐近恒定的下界，以及（2）GEOF的最低已知上界，这是第一个呈指数衰减的上界，与混合（$AB$）负性相匹配。 此外，将上述方法与先前部分转置噪声过滤技术的推广相结合，可以计算出一个单一的$C$测量值，该测量值最大化纯化的$AB$量子纠缠。 除了期望这些类空 GEOA 和 GEOF 的行为在相互作用理论中仍然存在之外，目前的测量和优化技术适用于超出量子场的物理多体高斯态。 显示英文摘要

摘要： In a pure Gaussian tripartition, a range of entanglement between two parties ($AB$) can be purified through classical communication of Gaussian measurements performed within the third ($C$). To begin, this work introduces a direct method to calculate a hierarchic series of projective $C$ measurements for the removal of any $AB$ Gaussian noise, circumventing divergences in prior protocols. Next, a multimode conic framework is developed for pursuing the maximum (Gaussian entanglement of assistance, GEOA) or minimum (Gaussian entanglement of formation, GEOF) pure entanglement that may be revealed or required between $AB$. Within this framework, a geometric necessary and sufficient entanglement condition emerges as a doubly-enclosed conic volume, defining a novel distance metric for conic optimization. Extremizing this distance for spacelike vacuum entanglement in the massless and massive free scalar fields yields (1) the highest known lower bound to GEOA, the first that remains asymptotically constant with increasing vacuum separation and (2) the lowest known upper bound to GEOF, the first that decays exponentially mirroring the mixed $AB$ negativity. Furthermore, combination of the above with a generalization of previous partially-transposed noise filtering techniques allows calculation of a single $C$ measurement that maximizes the purified $AB$ entanglement. Beyond expectation that these behaviors of spacelike GEOA and GEOF persist in interacting theories, the present measurement and optimization techniques are applicable to physical many-body Gaussian states beyond quantum fields.