Fault-tolerant quantum computers hand pieces of each logical qubit to separate decoder modules and shared readout lines. How much does a piece reveal? We prove that for any region and any Pauli noise, including correlated noise, an observer's optimal advantage in learning a logical bit is exactly 1 - 2 P_fail, where P_fail is the failure probability of maximum-likelihood decoding confined to that region. Two lessons follow. Geometry, not noise, provides the protection: a region that misses a single column of the code learns exactly nothing at any noise level, while a region that spans the code is protected by noise only at impractical distances (d > 350 for one row at a 10^-3 flip rate). And width is a poor guide to risk: under i.i.d. noise a two-row strip learns exactly as little as one row, yet below threshold an eavesdropper needs a width growing only as ln d. Through the identity, the strip's operational threshold is the Nishimori point of the random-bond Ising model, and a Walsh-Hadamard transfer matrix up to width 16 locates it to within a few thousandths. On two IBM Heron processors (d = 3, 5), an emulated strip adversary shows the predicted jump at width three, and non-uniform qubit errors let a trained attacker profit from the second row that uniform noise makes useless. We turn these results into design rules for partitioned decoding and multiplexed readout. Code and data are included.

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