Estimate distillable entanglement and quantum capacity by squeezing useless entanglement

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.