Geometry and local interfaces

Fix $L_0>0$, $T>L_0/c$, and $H>0$. Let

The source-to-wing paths are

They are strictly timelike. Each wing has a vertical retained storage path from time $T$ to $T+H$.

At $A$, there are qubits $Q_L,Q_R$ and a memory qubit $W$. The memory accompanies the left-moving register and is never measured or acted on by the payload. Its purpose is to make the retained quantum-information content completely explicit.

At $B_L$ and $B_R$, respectively, local input registers $S_L,S_R$ select between two measurement settings. These are local input ports, not remotely supplied control wires. Default preparations are product preparations.

The named quantum output is $Q_L{Q}_{R}W$, and the named classical outputs include the retained settings and the two locally acquired outcomes.