Toward the Goldilocks Blind Compression of Quantum States
Abstract
Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a k-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure n-qubit states, there exists a QAE with k encoder ancillas and n decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least k encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.
Related
- Exponential strong converse for blind quantum data compression
- Blind Quantum Computation with a Small Quantum Server
- Optimal compression with quantum retrieval
- The wiring sets a phase-blind quantum memory's gap, the weight caps its coherence
- Quantum Simulation of Non-Markovian Open Quantum Systems via Low-Rank Kernel Compression and Coupling Dilution
BibTeX
@misc{cha2026toward,
title = {{Toward the Goldilocks Blind Compression of Quantum States}},
author = {Hyunho Cha and Chae-Yeun Park and Jungwoo Lee},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.01258},
eprint = {2605.01258},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.01258},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Toward the Goldilocks Blind Compression of Quantum States
AU - Hyunho Cha
AU - Chae-Yeun Park
AU - Jungwoo Lee
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2605.01258
UR - https://arxiv.org/abs/2605.01258
AB - Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a k-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general \emph{completely positive and trace preserving} (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure n-qubit states, there exists a QAE with k encoder ancillas and n decoder ancillas that achieves the optimal fidelity over all CPTP encoder--decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least k encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.
ER -