Receiver-Constrained Recovery Placement for Encoded-Qutrit Teleportation under Monitored Decay

Abstract

Using established probabilistic measurement-reversal theory, we study recovery placement in encoded-qutrit teleportation under monitored decay. We characterize the success advantage of reversing a no-jump map only on the encoded support and compare two receiver capabilities. The restricted-map construction applies to general finite-dimensional supports; explicit timing results are obtained for a coherent V-type sender, a $Λ$-type receiver, and $S=\{0,2\}$, within a prescribed family of maximal exact sender reversals. With one outcome-independent full-space receiver filter, we maximize success probability at fixed total time subject to a minimum success-weighted conditional fidelity. A single preassigned recovery time yields up to three duration-dependent regimes: no sender reversal, the earliest feasible intermediate reversal, and final-time reversal. If recovery times may be randomized independently of the input and only the pooled successful ensemble must meet the fidelity requirement, the optimum over all such timing distributions mixes the two endpoints for $ΓT \ge (\ln 3)/2$. With Bell-outcome-dependent nonunitary receiver recovery, each accepted full-column-rank transfer branch can instead be reversed exactly. For the same model and sender-operation family, omitting sender reversal uniquely maximizes the exact-teleportation success probability for every finite $T>0$ at positive decay rate. Partial pathway coherence further distinguishes relative support gain from absolute recovery success: the long-time dark-state plateau survives only for fully coherent decay. These results show how receiver control capabilities and the meaning of the fidelity constraint determine whether intermediate sender recovery is useful.

The paper asks when a heralded sender-side reversal should be applied during encoded-state teleportation under monitored decay, and how the answer depends on receiver control and the fidelity constraint. It applies established probabilistic reversal theory to the restricted no-jump map $K_0Q$, giving optimal exact-recovery probability $\sigma_{\min}^2(K_0Q)$. This equals the full-space bound precisely when the encoded support intersects the minimum right-singular subspace. Explicit timing results concern a coherent $V$-type sender, a $\Lambda$-type receiver, and support $S=\{0,2\}$. With one fixed full-space receiver inverse, convexity and endpoint comparisons solve success maximization subject to a minimum success-weighted conditional fidelity: a single preassigned timing can favor no sender reversal, the earliest feasible intermediate reversal, or final-time reversal. If only pooled fidelity is constrained, optimization over all input-independent timing distributions yields an endpoint mixture for $\Gamma T\geq(\ln3)/2$. At $\Gamma T=2$ and fidelity $0.86$, randomization increases success from $1.01180\%$ to $1.28759\%$. With Bell-outcome-dependent nonunitary receiver recovery, each full-column-rank transfer branch is exactly reversible. Closed branch singular values show that omitting sender reversal uniquely maximizes success for every finite $T>0$ at positive decay rate within the prescribed sender family; success is $17.8933\%$ at $\Gamma T=2$. Timing claims assume ideal monitoring, independent Markovian baths, a noiseless resource partner, fixed encoding and Bell basis, and maximal exact sender reversals—not arbitrary controls. Partial pathway coherence removes the long-time recovery plateau. The supporting non-Markovian example treats uninterrupted evolution only; intermediate interventions require a multi-time description.