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Random unitaries, Robustness, and Complexity of Entanglement

Odavić, Jovan; Torre, Gianpaolo; Mijić, Nenad; Davidović, Davor; Franchini, Fabio; Giampaolo, Salvatore Marco (2023) Random unitaries, Robustness, and Complexity of Entanglement. Quantum, 7 . ISSN 2521-327X

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It is widely accepted that the dynamic of entanglement in presence of a generic circuit can be predicted by the knowledge of the statistical properties of the entanglement spectrum. We tested this assumption by applying a Metropolis-like entanglement cooling algorithm generated by different sets of local gates, on states sharing the same statistic. We employ the ground states of a unique model, namely the one-dimensional Ising chain with a transverse field, but belonging to different macroscopic phases such as the paramagnetic, the magnetically ordered, and the topological frustrated ones. Quite surprisingly, we observe that the entanglement dynamics are strongly dependent not just on the different sets of gates but also on the phase, indicating that different phases can possess different types of entanglement (which we characterize as purely local, GHZ-like, and W-state-like) with different degree of resilience against the cooling process. Our work highlights the fact that the knowledge of the entanglement spectrum alone is not sufficient to determine its dynamics, thereby demonstrating its incompleteness as a characterization tool. Moreover, it shows a subtle interplay between locality and non-local constraints.

Item Type: Article
Uncontrolled Keywords: quantum entanglement ; one-dimensional Ising chain ; Metropolis Monte Carlo ; Reny-2 entropy
Subjects: NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Condensed Matter Physics
Divisions: Center for Informatics and Computing
Theoretical Physics Division
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Depositing User: Fabio Franchini
Date Deposited: 27 Feb 2024 11:30
DOI: 10.22331/q-2023-09-15-1115

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