Quantum Teleportation in Non-equilibrium Environments and Fixed-point Fidelity

TL;DR

This work analyzes quantum teleportation in non-equilibrium environments using the Bloch-Redfield master equation to capture steady-state and transient dynamics of two coupled qubits interfaced with bosonic or fermionic reservoirs. It demonstrates that non-equilibrium conditions can enhance teleportation fidelity beyond equilibrium values and that fixed-point fidelity, where fidelity is independent of input states, can arise under specific parameter lines, further boosted by detuning between qubits. The study covers both steady-state resources and transient states, revealing regimes where non-equilibrium and detuning jointly maximize fidelity and identifying practical pathways to simplify quantum teleportation implementations in realistic noisy settings. The results provide guidance for robust quantum communication in non-ideal environments and highlight the fixed-point mechanism as a promising route toward reliable, input-state-independent teleportation.

Abstract

Quantum teleportation, a fundamental protocol in quantum information science, enables the transfer of quantum states through entangled particle pairs and classical communication channels. While ideal quantum teleportation requires maximally entangled states as resources, real-world implementations inevitably face environmental noise and decoherence effects. In this work, we investigate quantum teleportation in non-equilibrium environments with different temperatures or chemical potentials. We apply the Bloch-Redfield equation to characterize the non-equilibrium dynamics. In both bosonic and fermionic setups, the fidelity can be enhanced beyond the equilibrium values. Under specific non-equilibrium conditions, the fidelities of all input states are identical. We call it teleportation with a fixed-point fidelity. Notably, at the fixed-point, fidelity can also be enhanced by combining the two detuned qubits and non-equilibrium environments. These findings provide important guidance for implementing quantum communication protocols in realistic environments, while the fixed-point mechanism offers a promising pathway toward simplifying practical quantum teleportation schemes.

Figures (16)

• Figure 1: Maximum teleportation fidelity with the steady state of weak coupling system under the bosonic environments in terms of (a) the non-equilibrium condition $\Delta T= T_A - T_B$ or (b) the detuned energy level $\Delta\varepsilon = \varepsilon_A-\varepsilon_B$. The average temperature is set as low with $\bar{T}=1$ (black solid line), moderate with $\bar{T}=5$ (red dashed line) or high with $\bar{T}=10$ (green dashed dot line). The interaction strength is set as $\lambda = 6$. Other parameters are set as $\bar{\varepsilon}=10$ and $g_A=g_B=0.05$.
• Figure 2: Maximum teleportation fidelity of the steady state under the bosonic environments in terms of (a) the non-equilibrium condition $\Delta T= T_A - T_B$ or (b) the detuned energy level $\Delta\varepsilon = \varepsilon_A-\varepsilon_B$. The average temperature is set as low with $\bar{T}=1$ (black solid line), moderate with $\bar{T}=5$ (red dashed line) or high with $\bar{T}=10$ (green dashed dot line). The interaction strength is set as $\lambda = 30$. Other parameters are set as $\varepsilon_A=\varepsilon_B=10$ and $g_A=g_B=0.05$.
• Figure 3: The fidelity of four teleported states and the maximal average fidelity $\bar{F}_{max}$ (black solid line) in terms of the system's energy levels detuning $\Delta \varepsilon=\varepsilon_A-\varepsilon_B$. The parameters $\theta$ of four teleported states are $\pi$ (cyan dashed dot dot), $\pi/2$ (red dashed line),$\pi/3$ (green dot line) and $\theta=2.421$ (blue dashed dot line). Other parameter are set as $T_A=T_B=2$, $\varepsilon_A=\varepsilon_B=10$ and $g_A=g_B=0.05$.
• Figure 4: (a) The color-filled contour map shows the maximal fidelity in terms of the asymmetric energy detuning $\Delta \varepsilon=\varepsilon_A-\varepsilon_B$ and the non-equilibrium environment with temperature difference $\Delta T=T_A-T_B$. The two lines in (a) stand for the fixed-point fidelity and the corresponding fidelities $\bar{F}_{11}$ are shown in (b). The horizontal line at 0.95284 marks the peak of $\bar{F}_{11}$, while the vertical dashed line represents the corresponding $\Delta T$ value $\pm0.4752$. The parameters are set as $T_A=T_B=2$, $\varepsilon_A=\varepsilon_B=10$, $\lambda=30$ and $g_A=g_B=0.05$.
• Figure 5: The maximal average fidelity in terms the non-equilibrium chemical potential $\Delta \mu=\mu_A-\mu_B$. The average chemical potential is set as $\bar{\mu}=10$ (black solid line for $T=0.1$, red dashed line for $T=1$), $\bar{\mu}=12$ (green dash-dot line for $T=1$) and $\bar{\mu}=8$ (blued dot line for $T=1$). Other parameters are set as $\varepsilon_A=\varepsilon_B=10$, and $g_A=g_B=0.05$.