Insertion Correcting Capability for Quantum Deletion-Correcting Codes
This work provides theoretical insight into the error-correction capabilities of quantum codes for insertion and deletion errors, which is relevant for quantum communication and storage.
The paper proves that quantum t-deletion-correcting codes can also correct t insertion and deletion errors under a specific condition, and introduces the quantum indel distance to characterize this capability.
This paper proves that any quantum t-deletion-correcting codes also correct a total of t insertion and deletion errors under a certain condition. Here, this condition is that a set of quantum states is defined as a quantum error-correcting code if the error spheres of its states are disjoint, as classical coding theory. In addition, this paper proposes the quantum indel distance and describes insertion and deletion errors correcting capability of quantum codes by this distance.