Abstract

We specify and solve a finite sequential radiation model in which a qubit message is encoded in a degenerate source-energy sector. Explicit bounded Hamiltonians randomize the message with an independent two-bit key, emit the key into a first cell, and transfer the encrypted qubit into a second cell with a tunable probability. A separately tunable dephasing interaction supplies a complete coherence-loss control. Every inaccessible system, including the key purification and the dephasing environment, is retained in the complementary channel.

The full radiation channel, its action on all message matrix units, and an explicit decoder are calculated. Each individual emitted cell is exactly independent of the message, while the collective output can transmit the message perfectly. For transfer probability $p$ and coherence parameter $\eta$, the optimal worst-case recovery error is $(3-p-2p\eta )/4$, and the optimal maximally entangled test fidelity is $(1+p+2p\eta )/4$. The distance of a named complementary channel from a replacement channel is evaluated exactly.

Independent finite occupation ladders are emitted by additional energy-preserving Hamiltonians. Their amplitudes are calibrated to clipped geometric packet laws from the Em03-A–C interface. We prove the occupation-state, count-law, and mean comparisons, while distinguishing those comparisons from agreement of the full information-bearing radiation state. An explicit finite coherent access construction and bounded-generator implementation estimates give end-to-end recovery and destructive-record certificates. Entropy, reference mutual information, and recovery fidelity are reported separately.

The construction is a designed finite dynamical information-transfer model. It does not derive the interactions from quantum gravity, identify the cells with a local Schwarzschild evaporation process, or resolve horizon-smoothness and evaporation-endpoint questions.