Krylov Complexity and Mixed-State Phase Transition

2025/10/26 by Teh, Hung-Hsuan, Orito, Takahiro
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2510.22542

Abstract

We establish a unified framework connecting decoherence and quantum complexity. By vectorizing the density matrix into a pure state in a double Hilbert space, a decoherence process is mapped to an imaginary-time evolution. Expanding this evolution in the Krylov space, we find that the n-th Krylov basis corresponds to an n-error state generated by the decoherence, providing a natural bridge between error proliferation and complexity growth. Using two dephasing quantum channels as concrete examples, we show that the Krylov complexity remains nonsingular for strong-to-weak spontaneous symmetry-breaking (SWSSB) crossovers, while it exhibits a singular area-to-volume-law transition for genuine SWSSB phase transitions, intrinsic to mixed states.

Citations

• Simulation of bilayer Hamiltonians based on monitored quantum trajectories
• Topological Holography for Mixed-State Phases and Phase Transitions
• Mixed-state phases from local reversibility
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Probing mixed-state phases on a quantum computer via Renyi correlators and variational decoding
• Rényi Markov length in one-dimensional non-trivial mixed state phases and mixed state phase transitions
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Hardness of observing strong-to-weak symmetry breaking
• Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
• Quantum Strong-to-Weak Spontaneous Symmetry Breaking in Decohered One Dimensional Critical States
• Strong-to-weak spontaneous symmetry breaking and average symmetry protected topological order in the doubled Hilbert space
• Zipping many-body quantum states: a scalable approach to diagonal entropy
• Scheme to Detect the Strong-to-weak Symmetry Breaking via Randomized Measurements
• Fundamental thresholds for computational and erasure errors via the coherent information
• Generalized Loschmidt echo and information scrambling in open systems
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators
• Fluctuation-Dissipation Theorem and Information Geometry in Open Quantum Systems
• Krylov Complexity as a Probe for Chaos
• On Krylov Complexity
• Coherent information for CSS codes under decoherence
• Quantum Dynamics in Krylov Space: Methods and Applications
• Quantum Communication and Mixed-State Order in Decohered Symmetry-Protected Topological States
• Spontaneous Strong Symmetry Breaking in Open Systems: Purification Perspective
• Stability of mixed-state quantum phases via finite Markov length
• Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold
• Two-dimensional symmetry-protected topological phases and transitions in open quantum systems
• Mixed-state Quantum Phases: Renormalization and Quantum Error Correction
• Topological Phases with Average Symmetries: The Decohered, the Disordered, and the Intrinsic
• Geometry of Krylov Complexity
• Quantum phases of matter on a 256-atom programmable quantum simulator
• The ITensor Software Library for Tensor Network Calculations
• Quantum Computing in the NISQ era and beyond
• The density-matrix renormalization group in the age of matrix product states
• The large deviation approach to statistical mechanics
• Decoherence and the transition from quantum to classical -- REVISITED
• Completely positive linear maps on complex matrices
• Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet

Related

• Krylov Complexity for Open Quantum System: Dissipation and Decoherence
• Krylov Complexity in Mixed Phase Space
• Complexity and Operator Growth for Quantum Systems in Dynamic Equilibrium
• Universal Growth of Krylov Complexity Across A Quantum Phase Transition
• Non-perturbative saturation of Krylov complexity, and its implications in quantum gravity