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This theoretical paper derives a universal time-optimal generator for converting one quantum state into another under fixed-norm evolution, along with quantum speed limits for mixed states governed by Lindbladians and non-Hermitian Hamiltonians. The bounds apply to arbitrary system sizes and depend only on generator norms and state properties. For quantum readers, the practical value is a more general framework for estimating how fast quantum operations can run, which bears on control and gate-design limits, though it remains foundational work with no immediate hardware implications.
Time-optimal quantum dynamics under fixed-norm generators
arXiv:2610.42131v1 Announce Type: new Abstract: We investigate the dynamics of quantum systems whose evolution is governed by linear generators of fixed unitarily invariant norm. For this broad class of evolutions, we derive a universal time-optimal generator of the dynamics converting one given state into another. It provides a time-optimal non-Hermitian Hamiltonian for pure state conversion. We then use this general result to derive quantum speed limits for mixed-state evolutions governed by Lindbladians and non-Hermitian Hamiltonians. Our findings follow from the geometric properties of the group $GL(n,\mathbb{C})$, in particular the geodesic distance. The derived bounds hold for an arbitrary system size $n$, depend only on the norms of the evolution generator and the initial and final states, and do not require performing any time-averaging.
Abstract:We investigate the dynamics of quantum systems whose evolution is governed by linear generators of fixed unitarily invariant norm. For this broad class of evolutions, we derive a universal time-optimal generator of the dynamics converting one given state into another. It provides a time-optimal non-Hermitian Hamiltonian for pure state conversion. We then use this general result to derive quantum speed limits for mixed-state evolutions governed by Lindbladians and non-Hermitian Hamiltonians. Our findings follow from the geometric properties of the group $GL(n,\mathbb{C})$, in particular the geodesic distance. The derived bounds hold for an arbitrary system size $n$, depend only on the norms of the evolution generator and the initial and final states, and do not require performing any time-averaging.
arXiv:2610.42131 [quant-ph]
(or arXiv:2610.42131v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.42131 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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