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The quantum speed limit describes how quickly a quantum system can evolve intime from an initial state to a final state under a given dynamics. Here, wederive a generalised quantum speed limit (GQSL) for arbitrary time-continuousevolution using the geometrical approach of quantum mechanics. The GQSL isapplicable for quantum systems undergoing unitary, non-unitary, completelypositive, non-completely positive and relativistic quantum dynamics. Thisreduces to the well known standard quantum speed limit (QSL), i.e., theMandelstam-Tamm bound when the quantum system undergoes unitary time evolution.Using our formalism, we then obtain a quantum speed limit for non-Hermitianquantum systems. To illustrate our findings, we have estimated the quantumspeed limit for a time-independent non-Hermitian system as well as for atime-dependent non-Hermitian system namely the Bethe-Lamb Hamiltonian forgeneral two-level system.

Generalised quantum speed limit for arbitrary time-continuous evolution