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 $N_shots = 1000$. 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\(N_q{+}1\)/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.