Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits

• URL: http://arxiv.org/abs/2407.03206v2
• Date: Tue, 26 Nov 2024 10:18:52 GMT
• Title: Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Authors: Guanglei Xu, Yu-Xiang Zhang,
• Abstract summary: We find a series of new results about steady-state phase transitions, critical properties, and entanglement dynamics. For $textGHZ_3$ entanglement, we identify a measurement-induced transitions between a phase with finite amount of entanglement and a phase with no such entanglement. For multipartite $textGHZ_ngeq 4$ entanglement, we find that they emerge exclusively at the measurement-induced criticality.
• Score: 1.944801107374593
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• Abstract: We revisit the standard monitored random Clifford circuits from the perspective of $n$-partite Greenberger-Horne-Zeilinger ($\text{GHZ}_n$) entanglement, and find a series of new results about steady-state phase transitions, critical properties, and entanglement dynamics. For $\text{GHZ}_3$ entanglement, we identify a measurement-induced transitions between a phase with finite amount of $\text{GHZ}_3$ entanglement and a phase with no such entanglement. This transition also depends on how the system is divided into three parties: A partitioning-induced phase transition is observed in circuits with open boundary condition. For multipartite $\text{GHZ}_{n\geq 4}$ entanglement, we find that they emerge exclusively at the measurement-induced criticality. For the dynamical aspect, we find that $\text{GHZ}_3$ entanglement does not grow gradually as the case of bipartite entanglement. Instead, it appears suddenly via a dynamical phase transition (DPT). Moreover, in some situations without measurements, it persists for a while and then dies through another DPT. These DPTs are not in the scope of standard formalism based on Loschmidt amplitude.

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