Scrambling Transition in a Radiative Random Unitary Circuit

Abstract

We study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment at a rate $p$. As a result, initially localized quantum information not only spreads within the system, but also spills into the environment. Using the out-of-time-order correlator (OTOC) to characterize scrambling, we find a nonequilibrium phase transition in the directed percolation universality class at a critical swap rate $p_c$: for $p<p_c$ the ensemble-averaged OTOC exhibits ballistic growth with a tunable light cone velocity, while for $p>p_c$ the OTOC fails to percolate within the system and vanishes uniformly within a finite timescale, indicating that all local operators are rapidly swapped into the environment. To elucidate its information-theoretic consequences, we demonstrate that the transition in operator spreading coincides with a transition in an observer's ability to decode the system's initial quantum information from the swapped-out, or "radiated," qubits. We present a simple decoding scheme which recovers the system's initial information with perfect fidelity in the nonpercolating phase, and with continuously decreasing fidelity with decreasing swap rate in the percolating phase. Depending on the initial state of the swapped-in qubits, we further observe a corresponding entanglement transition in the coherent information from the system into the radiated qubits.

7+13 pages, 2+6 figures; v2: published version, improved clarity, modified references

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• Interactions and integrability in weakly monitored Hamiltonian systems
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Operator growth and spread complexity in open quantum systems
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Measurement-induced phase transition in teleportation and wormholes
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
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• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors
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• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Entanglement transitions induced by quantum-data collection
• Quantum chaos in the Dicke model and its variants
• An operational definition of quantum information scrambling
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Random Quantum Circuits with Time-Reversal Symmetry
• Monitored Fluctuating Hydrodynamics
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• Open-system dynamics in local Lindbladians with chaotic spectra
• Markovian to non-Markovian phase transition in the operator dynamics of a mobile impurity
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model