Effect of initial intrasystem entanglement on entropy growth in generalized Jaynes-Cummings models

TL;DR

This work shows that initial intrasystem entanglement tends to amplify entropy production in generalized Jaynes–Cummings models when interacting with a photonic environment. By analyzing ensembles of Haar-random pure and mixed states, along with energy-constrained and photon-number–restricted conditions across two- and three-level atoms, the authors quantify how the time-averaged entropy $\overline{S}_t$ correlates with entanglement measures like the Meyer–Wallach $Q$ and concurrence. The key finding is a robust, predominantly positive relationship between initial internal correlations and entropy growth, though the fractional contribution $\eta^{ent}$ depends on system size, environment photon number, and initial state purity; mixed states and higher photon numbers can reduce this contribution. These results deepen our understanding of entropy production in open quantum systems and underscore the significance of intrasystem correlations for quantum information processing and related foundational questions such as quantum Darwinism.

Abstract

We investigate how initial intrasystem entanglement influences the entropy generated in atomic systems interacting with a photonic environment in several generalizations of the Jaynes-Cummings model with two or more subsystems. Since the initial entanglement does not uniquely determine the final entropy, we focus on ensemble-averaged behavior. We consider ensembles of initial system states including pure and mixed Haar-random states, ensembles with fixed average energy or fixed mixedness, and varying initial photon numbers in the environment. In all cases, we observe a positive correlation between the initial entanglement and the entropy growth, although the fractional contribution of the initial entanglement varies. Our results emphasize the role of intrasystem correlations as a factor contributing to entropy growth in quantum informational processes.

Figures (5)

• Figure 1: Time-averaged entropy versus initial entanglement, quantified by the Meyer-Wallach measure. The atomic systems are initially prepared in Haar-random pure states. Different colors correspond to different numbers of subsystems. The average curves (solid lines) closely follow the fitting straight lines (dashed).
• Figure 2: Time-averaged entropy versus initial entanglement, quantified by the Meyer-Wallach measure, for pure initial system states with different fixed values of $\left\langle {E_i} \right\rangle$, indicated by different colors. Results for samples with the corresponding values of $\left\langle {E} \right\rangle$ are shown in gray. The groups of points corresponding to equal $\left\langle {E_i} \right\rangle$ and $\left\langle {E} \right\rangle$ substantially overlap.
• Figure 3: Time-averaged entropy versus initial entropy of entanglement for pure Haar-random initial system states and different initial photon numbers (indicated by different colors). The system consists of atoms with (a) a ground and a single excited level, and (b) a ground and two excited levels. The bold dots indicate the mean values for ensembles of random separable states.
• Figure 4: Time-averaged entropy change versus initial concurrence for initial Haar-random mixed states of the system and for different environment states (indicated by different colors). Solid lines correspond to the mean curves, while dashed lines represent the fitting lines.
• Figure 5: Time-averaged entropy change versus initial concurrence for samples with fixed initial mixedness of the system, measured by von Neumann entropy. Colors indicate different mixedness values. The environment is initially in the state $\ket{22}$.