Entanglement recovery by reversing the effect of noise in quantum repeater

Abstract

We propose a method to directly recover the degree of entanglement distributed by entanglement swapping in the presence of noise. Our approach introduces a reversing operation that probabilistically undoes the effect of amplitude damping or photon loss on a single entangled pair, enabling heralded recovery of entanglement. We demonstrate that entanglement can be substantially recovered even under strong noise, including parameter regimes where the distributed entanglement would otherwise vanish due to entanglement sudden death. We analyze the effectiveness of the protocol in two representative repeater models, i.e.,~two-way and one-way architectures and identify the optimal reversing strategy. Due to its heralded and single-copy nature, our protocol is readily compatible with other entanglement recovery techniques such as entanglement purification and distillation. Our work provides a practical and experimentally feasible way toward robust entanglement distribution in current and near-term quantum repeater architectures.

Figures (6)

• Figure 1: Reversing the effect of decoherence on entangled pair.
• Figure 2: (a) Concurrence of a single entangled pair under amplitude-damping decoherence. The dashed line shows the decay of concurrence as a function of the damping strength $D$, while the solid line shows the recovered concurrence obtained by applying the optimal reversing operation. (b) Success probability of the optimal reversing operation as a function of $D$.
• Figure 3: Two quantum repeater models: a two-way protocol based on entanglement swapping and a one-way protocol based on quantum teleportation, each consisting of a single repeater node. In the two-way model, the intermediate qubits $B$ and $C$ (shown in red) are assumed to undergo amplitude-damping decoherence before the Bell-state measurement (BSM). In the one-way model, the transmitted qubits $B$ and $D$ in the relay teleportation protocol are assumed to experience amplitude damping (shown in red). In our scheme, reversing operations are applied at each repeater node prior to the Bell-state measurements to undo the effects of noise.
• Figure 4: (a)–(c) for the $\Phi^{\pm}$ outcomes in the two-way repeater model: (a) Concurrence of the resulting distributed state as a function of $R$ for different damping strengths $D$. (b) Concurrence by optimal reversing operation as a function of $D$, where the dashed line denotes the concurrence decay without reversing operation, which vanishes at $D=0.5$, while the solid line shows the recovered concurrence, demonstrating that entanglement can be effectively restored even in the damping region where entanglement sudden death (ESD) occurs. The concurrence for the $\Psi^{\pm}$ outcomes ($C_{\Psi}$) and the concurrence averaged over all outcomes ($C_{\mathrm{ave}}$) are shown as the dotted and dot-dashed lines, respectively, for comparison. (c) Cost of Bell pairs required to recover entanglement via the optimal reversing operation for the $\Phi^{\pm}$ outcomes (solid line). The cost via entanglement swapping alone for the $\Psi^{\pm}$ outcomes ($Q_{\Psi}$) and the cost for obtaining the average concurrence over all outcomes ($Q_{\mathrm{ave}}$) are shown as the dotted and dot-dashed lines, respectively, for comparison.
• Figure 5: (a)–(c) for the $\Phi^{\pm}$ outcomes and (d)–(f) for the $\Psi^{\pm}$ outcomes in the one-way repeater model: (a) Concurrence of the resulting distributed state as a function of $R$ for different damping strengths $D$. (b) Concurrence by optimal reversing operation as a function of $D$, where the dashed and solid lines denote the unrecovered and recovered cases, respectively. (c) Cost of Bell pairs required to recover entanglement by the optimal reversing operation against amplitude damping. (d) Concurrence of the resulting distributed state as a function of $R$ for different damping strengths $D$. (e) Recovered concurrence by reversing operation with different strengths $R$ as a function of the amplitude damping $D$, where the unrecovered concurrence vanishes at $D\approx0.618$. (f) Cost of Bell pairs required to recover entanglement by the reversing operation with different strengths $R$ against amplitude damping.