Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states

• URL: http://arxiv.org/abs/2408.07794v1
• Date: Wed, 14 Aug 2024 20:10:39 GMT
• Title: Characterizing Optimal-speed unitary time evolution of pure and quasi-pure quantum states
• Authors: John A. Mora Rodríguez, Brian Grajales, Marcelo Terra Cunha, Lino Grama,
• Abstract summary: We show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $SU(n)/textnormalS(textnormalU(1)times textnormalU(n-1))$. We later extend that result to quasi-pure quantum states.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a characterization of the Hamiltonians that generate optimal-speed unitary time evolution and the associated dynamical trajectory, where the initial states are either pure states or quasi-pure quantum states. We construct the manifold of pure states as an orbit under the conjugation action of the Lie group $\SU(n)$ on the manifold of one-dimensional orthogonal projectors, obtaining an isometry with the flag manifold $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1 ))$. From this construction, we show that Hamiltonians generating optimal-speed time evolution are fully characterized by equigeodesic vectors of $\SU(n)/\textnormal{S}(\textnormal{U}(1)\times \textnormal{U}(n-1))$. We later extend that result to quasi-pure quantum states.

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