Multipartite Entanglement in the Measurement-Induced Phase Transition of the Quantum Ising Chain

TL;DR

This paper explores how measurement-induced phase transitions in a monitored quantum Ising chain affect multipartite entanglement, revealing complex behaviors and phase boundaries beyond bipartite correlations.

Contribution

It demonstrates that measurement-induced phase transitions extend to multipartite entanglement and introduces the use of quantum Fisher information to analyze this phenomenon.

Findings

Multipartite entanglement shows phase boundaries similar to entanglement entropy.

Quantum jumps introduce a third phase with logarithmic entropy but bounded multipartiteness.

The transition behavior is consistent across different measurement regimes.

Abstract

External monitoring of quantum many-body systems can give rise to a measurement-induced phase transition characterized by a change in behavior of the entanglement entropy from an area law to an unbounded growth. In this Letter, we show that this transition extends beyond bipartite correlations to multipartite entanglement. Using the quantum Fisher information, we investigate the entanglement dynamics of a continuously monitored quantum Ising chain. Multipartite entanglement exhibits the same phase boundaries observed for the entropy in the post-selected no-click trajectory. Instead, quantum jumps give rise to a more complex behavior that still features the transition, but adds the possibility of having a third phase with logarithmic entropy but bounded multipartiteness.