Universal Spreading of Conditional Mutual Information in Noisy Random Circuits

Abstract

We study the evolution of conditional mutual information in generic open quantum systems, focusing on one-dimensional random circuits with interspersed local noise. Unlike in noiseless circuits, where conditional mutual information spreads linearly while being bounded by the lightcone, we find that noisy random circuits with an error rate $p$ exhibit superlinear propagation of conditional mutual information, which diverges far beyond the lightcone at a critical circuit depth $t_c\propto p^{-1}$. We demonstrate that the underlying mechanism for such rapid spreading is the combined effect of local noise and a scrambling unitary, which selectively removes short-range correlations while preserving long-range correlations. To analytically capture the dynamics of conditional mutual information in noisy random circuits, we introduce a coarse-graining method, and we validate our theoretical results through numerical simulations. Furthermore, we identify a universal scaling law governing the spreading of conditional mutual information.

References in corpus (49)

• Mixed State Entanglement and Quantum Error Correction
• Chaos and Quantum Thermalization
• Topological entanglement entropy
• Efficient classical simulation of slightly entangled quantum computations
• Detecting topological order in a ground state wave function
• Improved Simulation of Stabilizer Circuits
• Black holes as mirrors: quantum information in random subsystems
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Fast Scramblers
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Measurement-driven entanglement transition in hybrid quantum circuits
• "Squashed Entanglement" - An Additive Entanglement Measure
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Structure of states which satisfy strong subadditivity of quantum entropy with equality
• The entanglement of purification
• Quantum conditional mutual information and approximate Markov chains
• The mother of all protocols: Restructuring quantum information's family tree
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Operator space entanglement entropy in transverse Ising chain
• Faithful Squashed Entanglement
• Multiqubit Clifford groups are unitary 3-designs
• A decoupling approach to the quantum capacity
• Monotonicity of quantum relative entropy revisited
• Quantum Graphical Models and Belief Propagation
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Quantum Belief Propagation
• Accessing scrambling using matrix product operators
• Efficient classical simulation of noisy random quantum circuits in one dimension
• Decoupling with random quantum circuits
• Entanglement on mixed stabiliser states--I: Normal Forms and Reduction Procedures
• Matrix product operators and states: NP-hardness and undecidability
• Spurious topological entanglement entropy from subsystem symmetries
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Spurious Long-range Entanglement and Replica Correlation Length
• Information scrambling in chaotic systems with dissipation
• Speed limits and locality in many-body quantum dynamics
• Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
• Markov entropy decomposition: a variational dual for quantum belief propagation
• Quantum Approximate Markov Chains are Thermal
• Short random circuits define good quantum error correcting codes
• Universal lower bound on topological entanglement entropy
• Entanglement Dynamics of Noisy Random Circuits
• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
• Toy model of boundary states with spurious topological entanglement entropy
• Holographic duality between local Hamiltonians from random tensor networks

Cited by in corpus (4)

• Stability of mixed-state quantum phases via finite Markov length
• Causal and Non-Causal Revivals of Information: A New Regime of Non-Markovianity in Quantum Stochastic Processes
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Open-system dynamics in local Lindbladians with chaotic spectra