2025/08/21 by Yuanchen Zhao, Li Rao, Zhao, Yuanchen +4
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Field (mathematics) #Ising model #Noise (video) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Partition function (quantum field theory) #Phase (matter) #Phase transition #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum entanglement #Quantum many-body systems #Quantum phase transition #Quantum phases #Replica #Spectrum (functional analysis) #Symmetry (geometry) #Symmetry breaking
paper · pdf · doi:10.1103/q7hz-qcxz
published in Physical review. B./Physical review. B 113(17) (American Physical Society)
openalex publication_date 2026/04/29 · openalex created_date 2026/05/03 · openalex updated_date 2026/07/21
The preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy, yet its stability against realistic, non-commuting measurement noise remains a critical open question. Here, we systematically investigate the rich phase structure emerging from a minimal model of competing, non-commuting weak measurements: nearest-neighbor Ising (ZiZj) and single-qubit transverse (Xi) operators. We analyze three experimentally relevant scenarios based on which measurement outcomes are read out: complete readout, no readout, and partial readout. Using a replica mean-field theory for higher dimensions, complemented by numerical simulations in one dimension, we derive the complete finite-time and stationary phase diagrams. Our analysis reveals a striking dependence on the readout protocol. Complete readout yields a direct transition between a short-range entangled (SRE) phase and a pure LRE phase. No readout (pure decoherence) precludes entanglement but exhibits a strong-to-weak spontaneous symmetry breaking (SWSSB) transition into a classically ordered mixed state. Most intriguingly, partial readout interpolates between these limits, featuring a mixed-state phase transition where the system can become trapped in the SWSSB phase or, for weaker non-commutativity, undergo successive symmetry breaking to reach a mixed LRE phase. A novel technical contribution is the use of a channel-fidelity-based partition function that allows us to simultaneously characterize both entanglement and SWSSB order, revealing a deep interplay between them in the replica limit. These results provide a cohesive picture for understanding measurement phase transitions, SWSSB, and mixed-state phase transitions, offering crucial insights for designing robust state preparation protocols on noisy quantum devices.