Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout

• URL: http://arxiv.org/abs/2508.15280v1
• Date: Thu, 21 Aug 2025 06:12:15 GMT
• Title: Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Authors: Yuanchen Zhao, Li Rao, Dong E. Liu,
• Abstract summary: Preparation of long-range entangled (LRE) states via quantum measurements is a promising strategy.<n>Here, we investigate the rich phase structure emerging from a minimal model of competing, non-commuting weak measurements.<n>We analyze three experimentally relevant scenarios based on which measurement outcomes are read out.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 ($Z_iZ_j$) and single-qubit transverse ($X_i$) 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.

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