Random unitaries, Robustness, and Complexity of Entanglement

TL;DR

This paper investigates how the dynamics of entanglement in quantum states depend on phases and local operations, revealing that entanglement spectrum alone cannot fully predict entanglement behavior.

Contribution

It demonstrates that entanglement dynamics vary with phase and local gates, challenging the sufficiency of the entanglement spectrum as a predictive tool.

Findings

Entanglement dynamics depend on phase and local operations.

Entanglement spectrum alone is insufficient to predict dynamics.

Different phases exhibit distinct entanglement resilience.

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.