The evolution of quantum battery capacity of GHZ-like states under Markovian channels

TL;DR

This work analyzes the evolution of quantum battery capacity $\mathcal{C}(\rho;H)$ for tripartite GHZ and GHZ-like states under Markovian channels, providing closed-form expressions for single-shot, multi-shot, and tri-side noise scenarios across several channels. By leveraging Kraus decompositions and the eigenstructure of the evolved states under channels such as bit flip, phase flip, bit-phase flip, depolarizing, amplitude damping, and dephasing, the authors characterize phenomena including capacity freezing, sudden death, and nonmonotonic revival, with explicit dependence on channel parameters $p$ and $n$ and system energies $\epsilon^A,\epsilon^B,\epsilon^C$. Key findings show that GHZ states exhibit freezing under dephasing and amplitude damping (increasing $n$ accelerates freezing), while bit-phase flip and depolarizing channels can induce brief sudden death; GHZ-like states display enhanced stability under dephasing and parameter-dependent behavior under amplitude damping, with tri-side identical channels often preserving substantial capacity. These results provide analytical benchmarks for energy storage in noisy multipartite quantum batteries and highlight how channel type and interaction topology critically shape the usable energy in open quantum systems.

Abstract

Quantum battery has enormous potential for development, and quantum battery capacity is an important indicator of quantum battery. In this work, we mainly study the evolution of quantum battery capacity of GHZ state and GHZ-like states under Markovian channels in the tripartite system. We find that under the depolarizing channel and bit-phase flip channel, the battery capacity shows a brief sudden death of the capacity. And we also find that under the dephasing channel, the battery capacity gradually decreases and tends to a constant, that is, the frozen capacity. We show that the battery capacity monotonically decreases for GHZ state under the amplitude damping channel on the first subsystem. And we study the variation of capacity under the Markovian channels n times on the first subsystem using the GHZ state. We can observe that under the amplitude damping and dephasing channels, the battery capacity decreases and tends to a constant, i.e. frozen capacity, and the larger n, the earlier this phenomenon occurs. We also investigate the evolution of capacity under three independent same type Markovian channels. We have also conducted corresponding research on GHZ-like states.

Figures (10)

• Figure 1: Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5, \epsilon^B=0.3, \epsilon^C=0.1$ under bit flip channel ($\text{\em C}(\rho_{bf}^{'},H_{ABC})$), phase flip channel ($\text{\em C}(\rho_{pf}^{'},H_{ABC})$), bit-phase flip channel ($\text{\em C}(\rho_{bpf}^{'},H_{ABC})$), depolarizing channel ($\text{\em C}(\rho_{dep}^{'},H_{ABC})$), depasing channel ($\text{\em C}(\rho_{dp}^{'},H_{ABC})$) and amplitude damping channel ($\text{\em C}(\rho_{adc}^{'},H_{ABC})$) as a function of p.
• Figure 2: (a) Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5$, $\epsilon^B=0.3$ and $\epsilon^c=0.1$ under the phase flip channel $n$ times as a function of $p$. (b) Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5$, $\epsilon^B=0.3$ and $\epsilon^c=0.1$ under the dephasing channel $n$ times as a function of $p$.
• Figure 3: Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5, \epsilon^B=0.3, \epsilon^C=0.1$ under the amplitude damping channel $n$ times on the first subsystem as a function of $p$.
• Figure 4: Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5$, $\epsilon^B=0.3$ and $\epsilon^C=0.1$ under tri-side same type phase flip channel. (a) $\gamma=0.25$ (b) $\gamma=0.5$ (c) $\gamma=0.75$ (d) $\gamma=1$
• Figure 5: Quantum battery capacity evolution for GHZ state with $\epsilon^A=0.5$, $\epsilon^B=0.3$ and $\epsilon^C=0.1$ under tri-side same type phase flip channel $n$ times. (a) $\gamma=0.25$ (b) $\gamma=0.5$ (c) $\gamma=0.75$ (d) $\gamma=1$