A team of theoretical physicists has derived a quantum evolution generator that is time-optimal for converting a given initial state into a target state, when the norm of the generator is held fixed. The result applies to a broad class of dynamics governed by linear generators with unitarily invariant norm, and yields a time-optimal non-Hermitian Hamiltonian for pure-state conversion. The work is posted on the arXiv preprint server.

The starting point is geometric: the authors exploit the properties of the group GL(n,ℂ), in particular its geodesic distance, to characterise the fastest trajectory between two states. From there they obtain quantum speed limits for mixed-state evolutions described by Lindblad equations and by non-Hermitian Hamiltonians. The bounds hold for arbitrary system size n and depend only on the norms of the evolution generator and of the initial and final states, without requiring any time-averaging.

The relevance of the result lies in its generality. Conventional quantum speed limits are usually restricted to unitary evolutions or to particular cases, and often require averaging the energy or the norm of the generator along the trajectory. Here, the formulation in terms of the geodesic distance in GL(n,ℂ) absorbs that dependence into a single fixed norm, which simplifies the statement and makes it applicable to dissipative and non-Hermitian dynamics, relevant for open systems and for platforms with gain and loss.

Beyond the formal interest, the bounds could serve as a benchmark to assess the efficiency of quantum control protocols, state preparation, and the simulation of open dynamics. The work also raises the question of how closely the optimal generator can be approximated with realistic physical Hamiltonians, and how these limits behave in the presence of additional constraints, such as the locality of interactions or noise.