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 consider 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：纠缠蒸馏是量子信息处理中的关键问题，但如何估算可蒸馏纠缠及其密切相关的物理量——噪声量子信道的量子容量，仍然具有挑战性。本文提出通过压制态或量子信道中无用纠缠（这些贡献在可蒸馏纠缠或量子容量中应被忽略）来评估这两个量的方法。首先，我们考虑一种称为资源反向散度的通用资源度量，用于量化目标态与自由态集合的最小散度。进而引入纠缠的反向最大相对熵，并将其用于建立可蒸馏纠缠的高效可计算上界。我们将资源反向散度推广至量子信道，导出量子容量的上界。进一步，我们将该方法应用于研究实际噪声（如去极化噪声和振幅阻尼噪声）下最大纠缠态的纯化过程，并在单向可蒸馏纠缠的估算中取得了显著改进。本文给出的上界还为评估感兴趣量子比特信道（包括泡利信道和随机混合酉信道）的量子容量提供了有效基准。