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Toward the Goldilocks Blind Compression of Quantum States

NeurIPS 2026 · Probabilistic and scientific modeling › Variational and generative sampling · approach: Structured latent VAEs · 0 citations (OpenAlex)

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Shows that k encoder ancillas and n decoder ancillas universally suffice for optimal CPTP blind single-copy quantum state compression under infidelity, that the encoder threshold is sharp, and that isometric decoders are not universally optimal, though numerically near-optimal.

Problem

Minimal circuit width (ancilla counts) for quantum autoencoders to reach the information-theoretic optimum of blind single-copy compression of pure quantum states through a k-qubit bottleneck under average infidelity.

Approach

Shows that a QAE with k encoder ancillas and n decoder ancillas achieves the optimum over all CPTP encoder-decoder pairs, via extreme-point (Choi rank) arguments and Stinespring-style padding, and that k encoder ancillas are necessary in the worst case, while isometric decoders can be suboptimal.

Key results

• Theorem: for every pure-state source, an (n,k,k,n)-QAE attains the optimal CPTP fidelity; encoder threshold k is worst-case necessary.
• Proposition: for the phase-family source with n=2, k=1, isometric decoders achieve fidelity strictly below 3/4 while a CPTP decoder reaches at least 3/4.
• Numerically on MNIST-encoded states, isometric (n_E=n-k) and n_E=n-k+1 decoders show no noticeable infidelity difference, while gap to conventional QAE is clear.

Surprising findings

• Isometric decoders, though sufficient in many analytic and numerical cases, are not universally optimal for blind compression under infidelity.
• Numerical gap between isometric and non-isometric decoders is practically negligible despite the analytical counterexample.

Limitations

• Restricted to blind single-copy compression of pure states with infidelity loss; other objectives not covered.
• Empirical validation uses engineered datasets (MNIST-encoded, synthetic families) rather than physical many-body states.
• Tight universal decoder ancilla lower bound as function of n and k remains open beyond k=1.

Experimental setup

Datasets: MNIST

Benchmarks: MNIST-encoded quantum states mu_{1,0.1} source family

Metrics: average infidelity trace distance

Baselines: conventional QAE (n,k,0,n-k) zeta-QVAE isometric decoder

Builds on: Quantum autoencoder (Romero et al. 2017) Stinespring dilation Choi-Jamiolkowski representation Ruskai-Werner-Zhang extreme channels zeta-QVAE (Wang et al. 2025)

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