Fidelity Determines the Minimum Error of Quantum Recovery

arXiv:2611.07344v1 Announce Type: new Abstract: Even a recovery that maximizes worst-input entanglement fidelity can retain avoidable errors in subsequent measurements. Entanglement fidelity is the probability of passing a test of whether the state and its entanglement were preserved; infidelity is the probability of failing it. Operational error is the largest possible change in any measurement probability, quantified by the normalized diamond distance. For every finite-dimensional noise channel and fixed encoding, we prove that operational error and worst-input entanglement infidelity have the same minimum over all recovery operations.