Environment-assisted and weak measurement strategies for robust bidirectional quantum teleportation

Abstract: This paper presents strategies for enhancing the robustness of bidirectional quantum teleportation (BQT) through environment-assisted and weak measurement techniques. BQT is a crucial component of distributed quantum networks, allowing for the bilateral transfer of quantum information between two nodes. While perfect teleportation necessitates maximally entangled states, these are vulnerable to degradation due to inherent decoherence. We propose a BQT scheme that enables the bilateral transfer of arbitrary qubits between nodes via amplitude damping channels (ADC), aiming to optimize fidelity using weak measurements in the final step of the process. Environment-assisted measurements (EAM) are used to establish a four-qubit channel composed of two Bell states. We explore two situations: (I) where only the recovery qubits pass through amplitude damping channels and (II) where the entire four-qubit channel is subjected to ADC. Our findings demonstrate a balance between average fidelity and success probability when the weak measurement strength ($q_w$) is constrained by the decay rate ($p$), specifically $q_w \in {[0,p]}$. Perfect BQT is achieved when $q_w = p$, indicating complete suppression of ADC effects. On the other hand, a decline in both average fidelity and success probability is noted when the weak measurement strength surpasses the ADC strength, marking the prohibited domain as $q_w \in {(p,1]}$. Additionally, our secured BQT protocol consistently outperforms the unprotected scheme in both scenarios, highlighting the effectiveness of the proposed protection strategies.