Coherence-Limited Quantum Speed Limit UnifyingMargolus–Levitin and Lloyd Bounds

This work clarifies the relationship between two foundational principles in quantuminformation theory: the Margolus-Levitin (M-L) theorem on the maximum speedof state evolution and the Lloyd limit on computational rate. We demonstrate thatthe energy E in these bounds refers to the quantum transition energy of thesystem, not its bulk kinetic energy. By imposing the physical constraint that anyquantum operation must be completed within the system’s coherence time (τc), wederive a minimum energy threshold, Emin = πℏ/(2τc), required to achieve a singleobservable state change (an orthogonalization). Applying this minimum energy tothe Lloyd limit correctly shows that the maximum operational rate is 1/τc, meaningexactly one operation is possible within the coherence window at this energy floor.This reframes the limits not as a function of motion, but as a direct trade-offbetween the system’s coherence and the energy required for computation, offeringa physically grounded perspective for designing quantum processors.