Krylov Complexity and Mixed-State Phase Transition

• URL: http://arxiv.org/abs/2510.22542v2
• Date: Mon, 10 Nov 2025 14:45:39 GMT
• Title: Krylov Complexity and Mixed-State Phase Transition
• Authors: Hung-Hsuan Teh, Takahiro Orito,
• Abstract summary: We establish a unified framework connecting decoherence and quantum complexity.<n>By vectorizing the density matrix into a pure state in a double Hilbert space, a decoherence process is mapped to an imaginary-time evolution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Three-body interaction in a magnon-Andreev-superconducting qubit system: collapse-revival phenomena and entanglement redistribution [21.959817015002937]
  Three-body interactions are fundamental for realizing novel quantum phenomena beyond pairwise physics.<n>We propose a hybrid quantum architecture comprising a magnonic mode (in a YIG sphere), an Andreev spin qubit (ASQ), and a superconducting qubit (SCQ)<n>We show that the genuine tripartite entanglement is redistributed into bipartite entanglement between the two qubits, and vice versa, with the total entanglement conserved.
  arXiv  Detail & Related papers  (2025-12-10T14:44:32Z)
• Universal Growth of Krylov Complexity Across A Quantum Phase Transition [0.0]
  We study the spread complexity in the Krylov space of quantum systems driven across a quantum phase transition.<n>For the transverse field Ising model, we establish an exact link between the growth of complexity and the Kibble-Zurek defect scaling.
  arXiv  Detail & Related papers  (2025-10-15T18:00:00Z)
• Implementing a Universal Set of Geometric Quantum Gates through Dressed-State assisted STA [39.27725073249277]
  We analyze the implementation of single-qubit gates in a two-level system driven by a microwave field.<n>We show how the dynamical phase can be canceled to obtain purely geometric operations.<n>We extend the protocol to construct non two-qubit gates, highlighting its feasibility for scalable quantum information processing.
  arXiv  Detail & Related papers  (2025-09-10T16:14:34Z)
• Quantum complexity phase transition in fermionic quantum circuits [14.723621424225973]
  We develop a general scaling theory for Krylov complexity phase transitions on quantum percolation models.<n>For non-interacting systems across diverse lattices, our scaling theory reveals that the KCPT coincides with the classical percolation transition.<n>For interacting systems, we find the KCPT develops a generic separation from the percolation transition due to the highly complex quantum many-body effects.
  arXiv  Detail & Related papers  (2025-07-29T18:00:25Z)
• Emergence of cosmic structure from Planckian discreteness [47.03992469282679]
  In the standard paradigm the inhomogeneities observed in the CMB arise from quantum fluctuations of an initially homogeneous and isotropic vacuum state.<n>We propose an alternative paradigm in which such inhomogeneities are present from the very beginning.<n>Specifically, inhomogeneities in the quantum state at the Planck scale propagate into semiclassical inhomogeneities on CMB scales.
  arXiv  Detail & Related papers  (2025-06-18T12:33:31Z)
• Topological Phase Transitions and Mixed State Order in a Hubbard Quantum Simulator [36.556659404501914]
  Topological phase transitions challenge conventional paradigms in many-body physics.<n>We observe such a transition between one-dimensional crystalline symmetry-protected topological phases.<n>Our results demonstrate how topology and information influence quantum phase transitions.
  arXiv  Detail & Related papers  (2025-05-22T17:58:35Z)
• Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity [10.451635171062017]
  We study the emergence of nonchaotic dynamics in a quantum spin chain with a local non-Hermitian disorder.<n>As the disorder strength increases, the emergence of nonchaotic dynamics is qualitatively captured through the growth of Krylov complexity.
  arXiv  Detail & Related papers  (2025-01-27T12:09:49Z)
• State Dependent Spread Complexity Dynamics in Many-Body Localization Transition [0.0]
  We characterize the Many-Body Localization (MBL) phase transition using the dynamics of spread complexity and inverse participation ratio in the Krylov space. Our work sheds light on the efficacy of Krylov space dynamics in understanding phase transitions in quantum many-body systems.
  arXiv  Detail & Related papers  (2024-09-03T18:00:11Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework.<n>This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.<n>Our findings demonstrate universal properties at quantum criticality, such as nonanalytic behaviors of steady-state observables, divergence of correlation lengths, and closing of the imaginary-Liouville gap.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Krylov complexity of purification [0.0]
  purification can map mixed states into pure states and a non-unitary evolution into a unitary one by enlarging the Hilbert space.<n>We establish a connection between the complexities of mixed quantum states and their purification, proposing new inequalities among these complexities.
  arXiv  Detail & Related papers  (2024-08-01T18:00:00Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.