We study the exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we consider the maximal number of copies of any given target state that can be extracted exactly from many copies of any given initial state as a function of the exponential decay in the success probability, known as the converse error exponent. We give a formula for the optimal rate presented as an infimum over the asymptotic spectrum of LOCC conversion. A full understanding of exact asymptotic extraction rates between pure states in the converse regime thus depends on a full understanding of this spectrum. We present a characterization of spectral points and use it to describe the spectrum in the bipartite case. This leads to a full description of the spectrum and thus an explicit formula for the asymptotic extraction rate between pure bipartite states, given a converse error exponent. This extends the result on entanglement concentration in [1], where the target state is fixed as the Bell state. In the limit of vanishing converse error exponent, the rate formula provides an upper bound on the exact asymptotic extraction rate between two states, when the probability of success goes to 1. In the bipartite case, we prove that this bound holds with equality.

中文翻译：

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LOCC 变换的渐近谱

我们研究了通过局部运算和经典通信 (LOCC) 以及在此类通道下的渐近纠缠转换，将多部分纯量子态精确地、非确定性地转换为另一个。特别地，我们考虑了可以从任何给定初始状态的许多副本中准确提取的任何给定目标状态的最大副本数，作为成功概率指数衰减的函数，称为逆误差指数。我们给出了最佳速率的公式，该公式表示为 LOCC 转换渐近谱的下界。因此，完全理解逆向态中纯态之间的精确渐近提取率取决于对这个谱的充分理解。我们提出了光谱点的特征，并用它来描述二分情况下的光谱。这导致了对频谱的完整描述，因此给出了纯二分状态之间的渐近提取率的明确公式，给定了逆误差指数。这扩展了 [1] 中纠缠浓度的结果，其中目标状态固定为贝尔状态。在逆误差指数消失的极限中，当成功概率为 1 时，速率公式提供了两个状态之间精确渐近提取率的上限。在二分情况下，我们证明该界限成立。