Random unitaries, Robustness, and Complexity of Entanglement

Abstract

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.

14 pages, 11 figures, 1 table

References in corpus (16)

• Quantum Computing
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Random Quantum Circuits
• Measuring entanglement entropy of a generic many-body system with a quantum switch
• Multipartite Entanglement Signature of Quantum Phase Transitions
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Genuine Multipartite Entanglement in the Cluster-Ising Model
• Irreversibility and Entanglement Spectrum Statistics in Quantum Circuits
• Topological and nematic ordered phases in many-body cluster-Ising models
• Quantifying genuine multipartite correlations and their pattern complexity
• A single $T$-gate makes distribution learning hard
• Floating Phase in 1D Transverse ANNNI Model
• Simulating continuous symmetry models with discrete ones
• Random unitaries, Robustness, and Complexity of Entanglement
• Momentum-space analysis of multipartite entanglement at quantum phase transitions

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• Entanglement Transitions in Unitary Circuit Games
• Long-range entanglement and topological excitations
• Magic phase transition and non-local complexity in generalized $W$ State
• Random unitaries, Robustness, and Complexity of Entanglement
• Interplay between local and non-local frustration in the 1D ANNNI chain I -- The even case
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models