  The estimation of quantum entropies and distance measures, such as von
Neumann entropy, R\'enyi entropy, Tsallis entropy, trace distance, and
fidelity-induced distances like Bures distance, has been a key area of
research. This paper introduces a unified approach using Disentangling Quantum
Neural Networks (DEQNN) for estimating these quantities, leveraging continuity
bounds and disentanglement in the cost function design. Our mathematical proof
demonstrates that DEQNN can preserve quantum entropies and distances in smaller
partial states, making them suitable for further estimation. This method is
scalable to an arbitrary number of quantum states and is particularly effective
for less complex quantum systems. Numerical simulations validate our approach,
and we also discuss strategies to enhance trainability and avoid barren
plateaus.
