Role of syndrome information in scheduling teleportation

Quantum teleportation enables quantum information transmission but requires distribution of entangled resource states. Unfortunately, decoherence, caused by environmental interference during quantum state storage, can degrade quantum states, leading to entanglement loss in the resource state and reduction of the fidelity of the teleported information. In this work, we investigate the use of error correction and error syndrome information in scheduling teleportation at a quantum network node in the presence of multiple teleportation requests and finite rate of remote entanglement distribution. Specifically, we focus on the scenario where stored qubits undergo decoherence over time due to imperfect memories. To protect the qubits from resulting errors, we employ quantum encodings, and the stored qubits undergo repeated error correction, generating error syndromes in each round. These error syndromes can provide additional benefits as they can be used to calculate qubit-specific error likelihoods, which can then be utilized in making better scheduling decisions. By integrating error correction techniques into the scheduling process, our goal is to minimize errors and decoherence effects, thereby enhancing the fidelity and efficiency of teleportation in a quantum network setting.