Improvement of 2-EPP using quantum error correcting codes and binary search

In [6], the 2-EPPs using quantum error correcting codes (QECCs) and binary search were proposed and shown to have a high purification capability. This protocol maintains a balance between error-detection and correction capabilities by using QECCs to detect errors and binary search to correct a single error. However, when we construct a protocol from codes whose code-length is long, sharing entanglement efficiently is difficult because of an incapability to perform error correction despite an error-detection capability. In this paper, we propose a method to improve the capability of error correction by using binary search more than once. We also show the performance of the protocol, which consists of a (16, 6, 4) stabilizer code, and show that this method is useful in improving performance.