A fault-tolerant quantum computer runs behind a telemetry stream logging syndromes, decoder actions, resets and timing separately from the answer. Can it reveal the logical input? For a distance-d rotated surface-code memory on a fixed schedule of $
A fault-tolerant quantum computer runs behind a telemetry stream logging syndromes, decoder actions, resets and timing separately from the answer. Can it reveal the logical input? For a distance-d rotated surface-code memory on a fixed schedule of T=\Theta(d) rounds, under three stated hypotheses (sector-scalar honest backbone, transcript locality, Kotecky-Preiss smallness), the channel from logical qubit to transcript is e^{-\Theta(d)}-close in diamond norm to one that ignores the input. A statement of this kind follows generically from correctability-privacy duality. Anisotropy does not. Each logical axis pays the distance of its own coset, so under amplitude damping the computational-basis label is governed by the code's Z-distance d_Z\ge d_{\min} and not by the code distance. Two codes of quantum distance 1 make the gap concrete. A phase-flip code's X-syndrome transcript is exactly input-independent under unobserved damping, while a repetition code leaks at first order. A matched converse identifies the records that do expose it, among them a lattice-surgery parity readout. On a 156-qubit superconducting processor our sufficient certificate misses by 21.5\times, so the theorem cannot be invoked there. Measured directly, a d_Z=1 memory's record identifies its input with total variation \ge 0.927 under randomised, label-balanced acquisition. Holding the code fixed and varying the damping exposure reproduces the parameter-free law, with exponent 0.85\pm0.03 against a predicted 0.86. Randomized encoding returns the statistic to the floor at no two-qubit-gate cost. Fault tolerance does not grant transcript privacy. It relocates it, and only to the logical state, not to the circuit's identity.