Abstract

We connect an explicit five-qubit encoding, a declared boundary access interface, and a complete deterministic decoder to a simultaneous finite-data quantum-channel certificate. The encoding is printed entrywise and realized by a fixed Clifford circuit. A syndrome calculation proves privacy of every boundary set of at most two qubits. Every set of at least three qubits admits an explicitly constructed accessible decoder; the optimal half-diamond recovery error for the smaller sets is exactly $3/4$. The associated six-qubit state is proved perfect.

For implemented channels, all failed attempts and decoder branches are retained. Conditional fixed-sample validation using three Bell correlations gives simultaneous reference-preserving error bounds, with calibration allowances in the fidelity interval and channel-transfer allowances outside the square root. We derive the certificate-specific sample requirements, an exact binomial alternative, and a linear conversion for independently established Pauli channels, including a physically randomized task.

The paper also constructs a two-pentagon tensor network with an explicit normalization and accessible subsystem decoders. A finite-spectator extension of the three-correlation certificate bounds recovery of one logical factor on arbitrary referenced bulk inputs. No experimental dataset, executed simulation, successful compilation, gravitational dictionary, metric reconstruction, Page curve, or inherited characteristic quantum coefficient is claimed.