Reliable Quantum Communications based on Asymmetry in Purification and Coding

The reliable provision of entangled qubits is an essential precondition in a variety of schemes for distributed quantum computing. This is challenged by multiple nuisances, such as errors during the transmission over quantum links, but also due to degradation of the entanglement over time due to decoherence. The latter can be seen as a constraint on the latency of the quantum protocol, which brings the problem of quantum protocol design into the context of latency-reliability constraints. We address the problem through hybrid schemes that combine: (1) indirect transmission based on teleportation and purification; (2) direct transmission, based on quantum error correction (QEC). The intuition is that, at present, the quantum hardware offers low fidelity, which demands purification; on the other hand, low latency can be obtained by QEC techniques. It is shown that, in the proposed framework, the purification protocol gives rise to asymmetries that can be exploited by asymmetric quantum error correcting code (QECC), which sets the basis for unique hybrid purification and coding design. Our results show that ad-hoc asymmetric codes give, compared to conventional QEC, a performance boost and codeword size reduction both in a single link and in a quantum network scenario.