Coherence-Limited Quantum Speed Limit from Mandelstam–Tamm and Lloyd Bounds

We derive a coherence-limited quantum speed limit by combining the Mandelstam–Tamm orthogonalizationbound with Lloyd’s computational rate bound. Imposing that any quantum operationmust complete within the system’s coherence time τc yields a minimum energy uncertaintyΔEmin = πℏ/(2τc). Inserting this into Lloyd’s bound gives a maximum achievable operation rateat the energetic floor of Ops/smax = 1/τc. This result parallels the unification obtained with theMargolus–Levitin bound but shifts the physical interpretation from average transition energy toenergy uncertainty. We compare the two unifications and discuss experimental relevance.