Distinguishing multiple coexisting area-law phases under competing non-commuting measurements

Develop scalable and reliable methods to distinguish multiple coexisting area-law entanglement phases in monitored quantum circuits where the phases are driven by competition among non-commuting measurements, rather than only differentiating volume-law from area-law regimes.

Background

Measurement-induced phase transitions in monitored quantum circuits can occur not only between volume-law and area-law entanglement regimes but also between distinct area-law phases, such as trivial, long-range entangled, and symmetry-protected topological phases. These transitions are typically diagnosed by nonlinear entanglement quantities, creating significant experimental overhead due to post-selection requirements.

While several strategies (e.g., cross-entropy benchmarking, spacetime duality mappings, early-time dynamics, feedback protocols, error-correction perspectives, and shadow tomography) have been proposed to mitigate post-selection challenges, they largely target distinguishing volume-law from area-law phases. Extending these approaches to reliably differentiate multiple coexisting area-law phases created by competing non-commuting measurements remains unresolved, motivating the need for new classification or detection protocols.

References

However, most of these strategies are designed to distinguish between two specific phases, typically the volume-law and area-law regimes. Distinguishing multiple coexisting area-law phases driven by competing non-commuting measurements remains an open challenge.

— Post-Selection-Free Decoding of Measurement-Induced Area-Law Phases via Neural Networks  (2604.03550 - Yu et al., 4 Apr 2026) in Introduction, paragraph beginning “Various strategies have been proposed to mitigate or bypass the post-selection problem.”