Entanglement distillation is crucial in quantum information processing. But it remains challenging to estimate the distillable entanglement and its closely related essential quantity, the quantum capacity of a noisy quantum channel. In this work, we propose methods for evaluating both quantities by squeezing out useless entanglement within a state or a quantum channel, whose contributions are expected to be ignored for the distillable entanglement or the quantum capacity, respectively. We first introduce a general resource measure called the reverse divergence of resources to quantify the minimum divergence between a target state and the set of free states. We then introduce the reverse max-relative entropy of entanglement and apply it to establish efficiently computable upper bounds on the distillable entanglement. We also extend the reverse divergence of resources to quantum channels and derive upper bounds on the quantum capacity. We further apply our method to investigate purifying the maximally entangled states under practical noises, such as depolarizing and amplitude damping noises, and notably establish improvements in estimating the one-way distillable entanglement. Our bounds also offer useful benchmarks for evaluating the quantum capacities of qubit quantum channels of interest, including the Pauli channels and the random mixed unitary channels.

翻译：纠缠蒸馏在量子信息处理中至关重要，但估计可蒸馏纠缠及其密切相关的关键量——噪声量子信道的量子容量——仍具挑战。本文提出了评估这两种量的方法，通过压缩量子态或量子信道中的无用纠缠来实现，这些纠缠的贡献预期分别被忽略以用于可蒸馏纠缠或量子容量。我们首先引入一种称为资源反向散度的通用资源度量，量化目标态与自由态集合之间的最小散度；然后引入纠缠的反向最大相对熵，并应用其建立可蒸馏纠缠的高效可计算上界。我们还将资源反向散度扩展到量子信道，推导出量子容量的上界。进一步，我们应用该方法研究实际噪声（如退极化噪声与振幅阻尼噪声）下最大纠缠态的纯化问题，显著改进了单向可蒸馏纠缠的估计。我们的上界还为评估感兴趣量子比特信道（包括泡利信道与随机混合酉信道）的量子容量提供了有效基准。