title: Quantum error correction assisted by two-way noisy communication.
abstract: Pre-shared non-local entanglement dramatically simplifies and improves the performance of quantum error correction via entanglement-assisted quantum error-correcting codes (EAQECCs). However, even considering the noise in quantum communication only, the non-local sharing of a perfectly entangled pair is technically impossible unless additional resources are consumed, such as entanglement distillation, which actually compromises the efficiency of the codes. Here we propose an error-correcting protocol assisted by two-way noisy communication that is more easily realisable: all quantum communication is subjected to general noise and all entanglement is created locally without additional resources consumed. In our protocol the pre-shared noisy entangled pairs are purified simultaneously by the decoding process. For demonstration, we first present an easier implementation of the well-known EAQECC [[4, 1, 3; 1]]. Then, we construct for the first time a 1-error-correcting code of 4 physical qudits capable of encoding 1 qubit of information, which is impossible in standard quantum error correction, demonstrating that our protocol can also improve the encoding rate in some sense. A systematic construction of two-way-noisy-communication-assisted codes is also provided.
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.|Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore.
authors.forename: Zhuo
authors.initials: Z
authors.lastname: Wang
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore.|Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics of University of Science and Technology of China, Hefei, Anhui, 230026, China.
authors.forename: Sixia
authors.initials: S
authors.lastname: Yu
authors.affiliation: Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China.
authors.forename: Heng
authors.initials: H
authors.lastname: Fan
authors.affiliation: Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore.
authors.forename: C H
authors.initials: CH
authors.lastname: Oh