The underlying order induced by orthogonality and the quantum speed limit

• URL: http://arxiv.org/abs/2104.01802v2
• Date: Tue, 27 Jul 2021 01:06:24 GMT
• Title: The underlying order induced by orthogonality and the quantum speed limit
• Authors: Francisco J. Sevilla, Andrea Vald\'es-Hern\'andez, and Alan J. Barrios
• Abstract summary: A set of parameters $r_i$ provides the energy distribution of pure qutrits evolving towards a distinguishable state at a finite time. A non-trivial interrelation between $tau$ and the energy spectrum is revealed. The states determined by $r_i$ are likewise analyzed according to their quantum-speed limit.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We perform a comprehensive analysis of the set of parameters $\{r_{i}\}$ that provide the energy distribution of pure qutrits that evolve towards a distinguishable state at a finite time $\tau$, when evolving under an arbitrary and time-independent Hamiltonian. The orthogonality condition is exactly solved, revealing a non-trivial interrelation between $\tau$ and the energy spectrum and allowing the classification of $\{r_{i}\}$ into families organized in a 2-simplex, $\delta^{2}$. Furthermore, the states determined by $\{r_{i}\}$ are likewise analyzed according to their quantum-speed limit. Namely, we construct a map that distinguishes those $r_{i}$s in $\delta^{2}$ correspondent to states whose orthogonality time is limited by the Mandelstam--Tamm bound from those restricted by the Margolus--Levitin one. Our results offer a complete characterization of the physical quantities that become relevant in both the preparation and study of the dynamics of three-level states evolving towards orthogonality.

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