  Quantum Internet relies on quantum entanglement as a fundamental resource for
secure and efficient quantum communication, reshaping data transmission. In
this context, entanglement distillation emerges as a crucial process that plays
a pivotal role in realizing the full potential of the quantum internet.
Nevertheless, it remains challenging to accurately estimate the distillable
entanglement and its closely related essential quantity, the quantum capacity.
In this work, we consider a general resource measure known as the reverse
divergence of resources which quantifies the minimum divergence between a
target state and the set of free states. Leveraging this measure, we propose
efficiently computable upper bounds for both quantities based on the idea that
the useless entanglement within a state or a quantum channel does not
contribute to the distillable entanglement or the quantum capacity,
respectively. Our bounds can be computed via semidefinite programming and have
practical applications for purifying maximally entangled states under practical
noises, such as depolarizing and amplitude damping noises, leading to
improvements in estimating the one-way distillable entanglement. Furthermore,
we provide valuable benchmarks for evaluating the quantum capacities of qubit
quantum channels, including the Pauli channels and the random mixed unitary
channels, which are of great interest for the development of a quantum
internet.
