Two Applications of Causal-Relational Closure: Relation-Held Quantum Memory and Post-Hoc Entanglement Topology

Causal-relational closure (CRC) distinguishes fixed local events from relations that remain open until an admissible future operation completes them. Two applications are simulated within standard quantum mechanics. The first is a relation-held quantum memory. A write event leaves a uniformly random record and a maximally mixed mediator, so the information exists only as a relation completed when read. After the record is scrambled into a six-qubit environment and discarded, recovery through the environment reaches average fidelity 0.870. A qubit spread over six hardware qubits running an unrelated Bernstein–Vazirani computation is recovered exactly. Tworobust versions follow. In the first, the data occupies the logical qubit of a Bacon–Shor subsystem code and the computation its gauge qubits; with gate and check noise of probability 10^−3, the data error falls 10 and 78 times below an unprotected qubit for code distances three and five. In the second, carriers are replaced while the relation is open, protection narrows once a record fixes the read basis, and faults are closed at read time. Under carrier-ageing noise, the error of the recorded-basis readout falls 19 to 290 times below a static Bacon–Shor memory, and 6 to 102 times with ancilla-based extraction. The second application is a post-hoc entanglement topology for quantum key distribution: a relay closes the requested pairing after users record key bits. Halving the stored qubits doubles the tolerable request latency, and relay storage conditioned on basis records extends it ninefold for an honest relay when bit flips are twentyfold slower than dephasing.