Reusing Erasure-Biased OAM Diffusion as a Storage Resource: A Loop-Buffer Memory and Its Loss Budget (v2)

Abstract / Description A companion note introduced an orbital-angular-momentum (OAM) cat-qubit encoding in which local, nearest-neighbor mode-mixing along a propagation channel converts almost all population leakage into a detectable erasure, with logical bit-flips suppressed exponentially in L²/γ z. That note treated the OAM channel purely as a transmission link. Here we ask whether the same physics can be repurposed as a storage resource, using an existing fiber-loop recirculating buffer architecture to accumulate propagation length zN = N Lₗₒₒₚ over N round trips rather than a single pass. We combine the companion note's exact Bessel/Skellam erasure statistics with a second, independent error channel absent from that note: the photon loss intrinsic to real loop-buffer hardware (switch insertion loss, splices), characterized by a per-loop survival probability η. We show analytically and numerically that, under a mode-uniform loss approximation, this hardware loss factors out of the conditional logical error rate εL entirely—it degrades only the repetition overhead (yield), not the fidelity of successfully retrieved qubits. We derive a memory "lifetime" Nₘₐₓ(L), the number of round trips before εL crosses a target threshold, and show it scales approximately as L². Combining this with realistic loop-buffer loss figures (1.85 dB/loop from a recent experimental demonstration) versus an optimistic low-loss-switch scenario (0.46 dB/loop), we find the repetition-overhead cost of reaching a useful memory lifetime differs by four orders of magnitude between the two hardware regimes at $L=6$—an explicit, quantified statement of what loss budget is required before loop-based OAM storage becomes practical. This revision (v2) grounds a time-multiplexed ("FIFO pipeline") extension of the buffer in the same combined loss/diffusion model, replacing naive raw-pulse-rate-times-storage-time capacity estimates with the actual number of qubits recoverable at a target fidelity. We find that the realistic sustained useful throughput is orders of magnitude below such naive estimates, and is set almost entirely by the per-loop loss budget rather than by the OAM channel physics or the raw pulse repetition rate.