Tight Ancilla Bound for Quantum Autoencoders in State Reconstruction

Quantum autoencoders offer a principled way to reduce the quantum resources required to store and process quantum data, but the resources needed for reliable reconstruction can be as important as the size of the compressed representation itself. In particular, understanding the fundamental ancilla requirements is essential for determining whether a compressed quantum model can be realized within a given hardware budget. Prior work established that a unitary decoder with $n$ ancilla qubits is universally sufficient for compressing $n$-qubit states through a $k$-qubit bottleneck. It remained open, however, whether the full $n$-ancilla requirement can be necessary for arbitrary bottleneck sizes. We resolve this question in the affirmative. Thus, the universal $n$-ancilla upper bound is worst-case tight for every bottleneck size, revealing a symmetric resource requirement for the encoder and decoder in blind single-copy quantum compression.