Quantum Energy Teleportation under Equilibrium and Nonequilibrium Environments

TL;DR

This work investigates quantum energy teleportation (QET) for a two-qubit system coupled to equilibrium and nonequilibrium reservoirs. It derives analytical expressions for energy output in the eigenbasis and analyzes QET under Bloch–Redfield dynamics, including detuning and bath-asymmetry effects. A key finding is that mixed-state energy output often tracks the eigenstate with the largest population, while nonequilibrium environments can enhance $E_{out}$ in certain regimes, especially with detuning and asymmetric baths. These results highlight nonequilibrium engineering as a viable knob to improve energy extraction in QET and point to the need for generalized protocols that exploit multiple eigenstates simultaneously.

Abstract

Quantum energy teleportation (QET), implemented via local operations and classical communication, enables carrier-free energy transfer by exploiting quantum resources. While QET has been extensively studied theoretically and validated experimentally in various quantum platforms, enhancing energy output for mixed initial states, as the system inevitably interacts with environments, remains a significant challenge. In this work, we study QET performance in a two-qubit system coupled to equilibrium or nonequilibrium reservoirs. We derive an analytical expression for the energy output in terms of the system Hamiltonian eigenstates, enabling analysis of energy output for mixed states. Using the Redfield master equation, we systematically examine the effects of qubit detuning, nonequilibrium temperature difference, and nonequilibrium chemical potential difference on the energy output. We find that the energy output for mixed states often follows that of the eigenstate with the highest population, and that nonequilibrium environments can enhance the energy output in certain parameter regimes.

Figures (9)

• Figure 1: Energy output of four eigenstates of $H_{AB}$ (\ref{['HS']}). The parameters are set as $\kappa=1$ and $\varepsilon_A=\varepsilon_B=2$.
• Figure 2: Energy output of steady states in the equilibrium bosonic reservoirs and the corresponding population of $|E_1\rangle$. ($\text{a}_1$) Energy output when the energy levels are set as $\varepsilon= 0.1~ (\text{black solid line})$, $1~(\text{red dashed line})$, $5~(\text{green dot line})$ and $10~(\text{blue dashed dot line})$. ($\text{a}_2$) The population of $|E_1\rangle$ corresponding to ($\text{a}_1$). ($\text{b}_1$) Energy output when the temperatures are set as $T= 0.1~ (\text{black solid line})$, $1~(\text{red dashed line})$, $5~(\text{green dot line})$ and $10~(\text{blue dashed dot line})$. ($\text{b}_2$) The population of $|E_1\rangle$ corresponding to ($\text{b}_2$). The other parameters are set as $\kappa=1$ and $g_A=g_B=0.05$.
• Figure 3: (a) Energy output of steady states with increasing chemical potential in fermionic reservoirs. The parameters are set as $\varepsilon=1$ and $\theta=\theta_1$ (black solid line), $\varepsilon=1$ and $\theta=\theta_2$ (red dashed line), $\varepsilon=3$ and $\theta=\theta_1$ (green solid line), $\varepsilon=3$ and $\theta=\theta_2$ (blue dashed line). (b) The population of state $|E_4\rangle$ with $\mu$. The parameters are set as $\varepsilon=1$ (black solid line) or $\varepsilon=3$ (red dashed line). The other parameters are set as $\kappa=1$, $T = T_A=T_B=1$, and $g_A=g_B=0.05$.
• Figure 4: Energy output of steady states under the nonequilibrium bosonic environments or the energy detuning, and the corresponding population of eigenstates. ($\text{a}_1$) The average temperatures are set as $\bar{T}=0.5$ (black solid line), $\bar{T}=2$ (red dashed line), and $\bar{T}=5$ (green dot line). The energy levels are set as $\varepsilon_A=\varepsilon_B=2$. ($\text{a}_2$) The population of state $|E_1\rangle$ (in solid line) and state $|E_2\rangle$ (in dashed line) corresponding to ($\text{a}_1$). ($\text{b}_1$) The energy levels are set as $\bar{\varepsilon}=1$ with $T=0.5$ (black solid line), $\bar{\varepsilon}=2$ with $T=0.5$ (red dashed line), and $\bar{\varepsilon}=2$ with $T=2$ (green dot line). ($\text{b}_2$) The population of state $|E_1\rangle$ (in solid line) and state $|E_2\rangle$ (in dashed line) corresponding to ($\text{b}_1$). The other parameters are set as $\kappa=1$ and $g_A=g_B=0.05$.
• Figure 5: Energy output of steady states of two detuned qubits under the bosonic nonequilibrium environments. The parameters are set as $\bar{\varepsilon}=(\varepsilon_A+\varepsilon_B)/2=2$, $\bar{T}=(T_A+T_B)/2 = 0.5$, $\kappa=1$, and $g_A=g_B=0.05$.