Quantum Reservoir Autoencoder for Blind Decryption: Two-Phase Protocol and Noise Resilience

We instantiate the quantum reservoir autoencoder (QRA) with a noise-induced reservoir employing reset noise channels and address two open problems: noise-resilient reversibility and blind decryption. For a single-ciphertext protocol with 10 data qubits and random (non-optimized) reset probabilities, the open-system reservoir suppresses shot-noise sensitivity by ten orders of magnitude, yielding mean-squared error (MSE) $\sim {10}^{-14}$ compared with $\sim {10}^{-3}$ without reset channels ($N_{\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{t}\mathrm{s}}=1000$). A two-phase protocol trains per-position decoding weights from $M$ shared training plaintexts and decrypts previously unseen messages at MSE $\sim {10}^{-4}$, with no statistically significant performance difference among ideal, shot-noise, and reset-plus-shot-noise conditions ($p>0.05$, 16 seeds). Experiments at $N_q=5$, 7, and 10 reveal a sharp phase transition at plaintext length $N_c\approx N_q(N_q+1)\mathrm{/}2+8$, providing a design rule for the minimum qubit count. Two blind decoder variants that lack ground-truth targets – a single-ciphertext cross-path iteration (MSE $\approx 0.3$) and a multi-sample regression variant (MSE $\approx 0.53$, worse than random) – establish that shared training data is the irreducible requirement for blind decryption. A comparison with variational quantum circuit baselines shows that the fixed-reservoir analytic-readout architecture is dramatically more noise-robust: a quantum recurrent neural network protocol is completely destroyed under depolarizing noise, whereas the QRA remains invariant.