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arXiv · 2104.01802

The underlying order induced by orthogonality and the quantum speed limit

Francisco J. Sevilla·Andrea Valdés-Hernández·Alan J. Barrios
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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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Francisco J. Sevilla, Andrea Valdés-Hernández, Alan J. Barrios. 2021-04-05. The underlying order induced by orthogonality and the quantum speed limit. https://doi.org/10.3390/quantum3030024

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