Unequal Information Distribution in Holographic Quantum Codes

Under ideal Pauli-noise and noiseless-syndrome assumptions in our stabilizer-factorization model, the backward-boundary entropy reduction, hereby denoted ΔH, is known to be zero. Nevertheless, on real quantum hardware, we measure ΔH > 1 bit on every code tested, revealing structured entropy reduction from a calibration-based backward boundary. Comparing three distance-3 codes on the same IBM processor (a holographic [[5,1,3]] code, Steane [[7,1,3]], and Shor [[9,1,3]]), we find that this information distributes anisotropically across stabilizers on the holographic code (per-stabilizer variation 6.6–8.2% vs. isotropic controls; permutation test, p < 0.01). Two independent strength sweeps, one computational prior-concentration sweep and one physical measurement-strength sweep via tunable rotation gates, produce matching per-stabilizer rankings (Fisher p = 0.021), with the anisotropy gap peaking at 42× in an intermediate prior-concentration regime. Two controlled negatives (readout conditioning and repeated syndrome extraction) and a four-boundary ablation identify holographic geometry as the main distinguishing variable among the factors tested. These results, reproduced on two independent IBM quantum processors with different per-stabilizer rank orderings (combined p = 0.042), are consistent with the inhomogeneous boundary geometry predicted by holographic tensor network models of AdS/CFT.