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

Abstract

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 $L^2/\gamma z$. 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 $z_N = N L_{loop}$ 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 $\eta$. We show analytically and numerically that, under a mode-uniform loss approximation, this hardware loss factors out of the conditional logical error rate $\epsilon_L$ entirely—it degrades only the repetition overhead (yield), not the fidelity of successfully retrieved qubits. We derive a memory "lifetime" $N_{max}(L)$, the number of round trips before $\epsilon_L$ crosses a target threshold, and show it scales approximately as $L^2$. Combining this with realistic loop-buffer loss figures ($1.85 \text{ dB/loop}$ from a recent experimental demonstration) versus an optimistic low-loss-switch scenario ($0.46 \text{ dB/loop}$), 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.