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arXiv:0911.5729 · Physical Review A

Critical dynamics of decoherence

Bogdan Damski, H. T. Quan, Wojciech Hubert Zurek

Published Jun 9, 2011• 90 citations
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Abstract

We study decoherence induced by a dynamic environment undergoing a quantum phase transition. The environment's susceptibility to perturbations---and, consequently, the efficiency of decoherence---is amplified near a critical point. Over and above this near-critical susceptibility increase, we show that decoherence is dramatically enhanced by the nonequilibrium critical dynamics of the environment. We derive a simple expression relating decoherence to the universal critical exponents exhibiting deep connections with the theory of topological defect creation in nonequilibrium phase transitions.

DOI
10.1103/physreva.83.062104

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We study decoherence induced by a dynamic environment undergoing a quantum phase transition. The environment's susceptibility to perturbations---and, consequently, the efficiency of decoherence---is amplified near a critical point. Over and above this near-critical susceptibility increase, we show that decoherence is dramatically enhanced by the nonequilibrium critical dynamics of the environment. We derive a simple expression relating decoherence to the universal critical exponents exhibiting deep connections with the theory of topological defect creation in nonequilibrium phase transitions.
We study dynamics of decoherence in a generic model where the environment is driven and undergoes a quantum phase transition. We model the environment by the Ising chain in the transverse field, and assume that the decohering system is a central spin-1/2. We found that when the environment is quenched slowly through the critical point, the decoherence factor of the central spin undergoes rapid decay that encodes the critical exponents of the environment. We also found that decoherence in a non-equilibrated, kink-contaminated, environment can be stronger than in a vacuum one. We derived a remarkably simple analytical expression that describes post-transition decoherence and predicts periodicities involving all system parameters. This research connects the fields of decoherence, quantum phase transitions, and Kibble-Zurek non-equilibrium dynamics.
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics. We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment. We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition. If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power law.
We analyze the decoherence induced on a single qubit by the interaction with a two-level boson system with critical internal dynamics.We explore how the decoherence process is affected by the presence of quantum phase transitions in the environment.We conclude that the dynamics of the qubit changes dramatically when the environment passes through a continuous excited state quantum phase transition.If the system-environment coupling energy equals the energy at which the environment has a critical behavior, the decoherence induced on the qubit is maximal and the fidelity tends to zero with finite size scaling obeying a power-law.
Understanding how noise influences nonequilibrium quantum critical dynamics is essential for both fundamental physics and the development of practical quantum technologies. While the quantum Kibble-Zurek (QKZ) mechanism predicts universal scaling during quenches across a critical point, real quantum systems exhibit complex decoherence that can substantially modify these behaviors, ranging from altering critical scaling to completely suppressing it. By considering a specific case of nondemolishing noise, we first show how decoherence can reshape universal scaling and verify these theoretical predictions using numerical simulations of spin chains across a wide range of noise strengths. Then, we study linear quenches in the transverse-field Ising model on IBM superconducting processors where the noise model is unknown. Using large system sizes of 80-120 qubits, we measure equal-time connected correlations, defect densities, and excess energies across various quench times. Surprisingly, unlike earlier observations where noise-induced defect production masked universal behavior at long times, we observe clear scaling relations, pointing towards persistent universal structure shaped by decoherence. The extracted scaling exponents differ from both ideal QKZ predictions and analytic results for simplified noise models, suggesting the emergence of a distinct noise-influenced universality regime. Our results, therefore, point toward the possibility of using universal dynamical scaling as a high-level descriptor of quantum hardware, complementary to conventional gate-level performance metrics.
Phase transitions represent fundamental transformations of matter, characterized by abrupt changes in macroscopic properties and often associated with singular behavior at critical points. While equilibrium aspects of phase transitions, particularly universal critical exponents and scaling laws, are well-understood, the non-equilibrium processes occurring near criticality, especially the production of entropy, remain a rich area of investigation. This paper explores the intricate relationship between critical entropy production and the emergence of scaling laws in systems undergoing phase transitions. We delve into how the rate of entropy production diverges or exhibits anomalous scaling near critical points, reflecting the system's attempts to dissipate energy and respond to external perturbations as it approaches a state of macroscopic change. By integrating concepts from non-equilibrium thermodynamics, statistical mechanics, and renormalization group theory, we aim to elucidate the underlying mechanisms that govern entropy generation in these critical regimes. We discuss theoretical frameworks that predict universal scaling behaviors for entropy production rates, analogous to those observed for equilibrium order parameters and susceptibilities. The implications of these scaling laws extend beyond theoretical physics, offering insights into complex systems, far-from-equilibrium dynamics, and the efficiency of energy conversion processes in critical environments. Our analysis highlights the critical entropy production as a unique signature of non-equilibrium dynamics during phase transitions, providing a deeper understanding of the interplay between fluctuations, dissipation, and universality near points of instability.
In this paper, we have investigated the quantum entanglement of quantum states undergoing decoherence from a spin environment which drives a quantum phase transition. From our analysis, we find that the entanglement dynamics depends not only on the coupling strength but also on the external magnetic field and the number of the freedom degrees of the environment. Specially, our results imply that the decay of the entanglement can be enhanced by the quantum phase transition of the environment when the system is coupled to the environment weakly. Additionally, the discussion of the case of the multipartite states with high dimensions is made.