Quantum Correlation Dynamics Subjected to Quantum Reset-Driven Environment

TL;DR

The paper analyzes how stochastic quantum resetting of a driven Ising-chain environment affects entanglement and quantum discord between two central qubits. Using a central-spin model with a linearly ramped transverse field $h(t)=t/\tau$ and a reset mechanism applied at rate $r$, the environment decomposes into momentum modes, yielding a decoherence factor $D(t)$ that controls the reduced two-qubit state. In the reset-free case, strong coupling yields revival of quantum correlations between the Ising critical points $h_c=\pm1$, while weak coupling leads to monotonic decay; resetting introduces exponential suppression of concurrence revivals (with $C^{\max}$ scaling as $\exp(-\alpha r)$) and removes a universal scaling for quantum discord, instead producing oscillatory decay patterns whose period grows as $r$ or $\tau$ decreases. The results demonstrate that stochastic resetting can be a powerful control tool for shaping quantum resources in nonequilibrium many-body environments, with potential experimental implementations in trapped-ion, Rydberg, and superconducting platforms.

Abstract

We study two central qubits interacting with a transverse-field Ising chain that serves as their environment. The environment is driven linearly in time across its quantum critical points (QCPs) and, during the evolution, is subjected to quantum reset (QR), where it is returned at random times to its initial state. We investigate how such QR of the environmental spin chain modifies the dynamics of entanglement and quantum discord between the qubits. Our results show that in the strong-coupling regime, entanglement and discord exhibit pronounced revivals within the interval bounded by the Ising QCPs, but these revivals diminish as the QR rate increases. In contrast, weak coupling leads to a monotonic reduction of quantum correlations. Numerically, we find that the revival peaks of concurrence decay and scale exponentially with the QR rate, while quantum discord shows no clear scaling behavior. In the weak-coupling regime without QR, the correlations decay monotonically as the driven field crosses the second QCP. When QR is applied, however, both entanglement and discord undergo oscillatory suppression, with the oscillation period increasing as either the QR rate or the ramp time scale is reduced.

Figures (7)

• Figure 1: Schematic of the driven transverse-field Ising chain that serves as the environment for the two central qubits. For large $|h(t)|$, the chain is in the paramagnetic phase with spins aligned along the field (left and right panels). For $|h(t)|<1$ (center panel), the chain enters the ferromagnetic phase, where spins align along $\pm x$, spontaneously breaking the Ising symmetry. The qubits couple via their $z$ components to the environment, and the field $h(t)$ is ramped across the quantum critical points at $h=\pm1$.
• Figure 2: Concurrence ($C$) versus $h(t)=t/\tau$ in the absence of resetting, for chain size $N=500$, coupling $\delta=0.01$, and initial Werner parameter $a=0.9$. Panels correspond to different ramp times: (a) $\tau=250$ (strong coupling/slow ramp), (b) $\tau=1$, and (c) $\tau=0.1$ (weak coupling/fast ramp). In the slow-ramp regime, $C$ exhibits near-complete revivals between the critical points $h=\pm1$, whereas for shorter ramps it decays monotonically.
• Figure 3: Quantum discord (QD) versus $h(t)=t/\tau$ in the absence of resetting, with the same parameters as in Fig. 2. (a) For slow ramps ($\tau=250$), discord revives between the critical points, though less sharply than concurrence. (b,c) For intermediate and fast ramps ($\tau=1$, $\tau=0.1$), discord decays monotonically but remains finite even in regimes where concurrence vanishes.
• Figure 4: Concurrence versus $h(t)=t/\tau$ under stochastic resetting of the environment, for $N=500$, $\delta=0.01$, $a=0.9$, and reset rates $r$ as indicated. (a) Slow ramp ($\tau=250$): partial revivals persist between $h=\pm1$ but their amplitudes decrease with increasing $r$. (b) Intermediate ramp ($\tau=1$): revivals are suppressed and correlations decay more rapidly with $r$. (c) Fast ramp ($\tau=0.1$): correlations are strongly reduced and only weakly dependent on $r$.
• Figure 5: Quantum discord versus $h(t)=t/\tau$ under stochastic resetting, for the same parameters as in Fig. 4. Resetting suppresses revivals and accelerates decay, although discord remains finite even when concurrence vanishes. The effect of increasing $r$ is most visible in the slow-ramp case (a), while for faster ramps (b,c) the dynamics are dominated by monotonic suppression.