Unitary Quantum Error Correction without Error Detection

Abstract

We propose a quantum error correction without error detection. A quantum state $\rho_0$ combined with an ancilla state $\sigma$ is encoded unitarily and an error operator is applied on the encoded state. The recovery operation then produces a tensor product state $\rho_0 \otimes \sigma'$. The decoding operation is combined with the recovery operation and the state $\rho_0$ is directly reproduced without referring to the code word. A higher rank projection operator required for a conventional operator quantum error correction is not necessary to implement. Encoding and the recovery operations are implemented with unitary operators only, which makes quantum error correction much easier than any other proposals.