Solutions for Redundancy-Free Error Correction in Quantum Channel

All free-space quantum communications require the use of a quantum channel, which transports quantum bits in such a way that the quantum mechanical states of the qubits remain preserved from one end of the channel to the other one. In quantum computing the classical error coding methods could not be used, however we can construct a classical channel with zero redundancy error correction for any unitary channel. In our basically new quantum error correction approach, the classical states are coded into the eigenvectors and unitary transformations. In this paper, we show that with our new algorithm it’s possible to create redundancy-free quantum error correction. We also consider the redundancy-free implementation of a unitary error correcting operator. Our protocol achieves the redundancy-free quantum communication using local unitary operations and unitary matrices. These solutions could be useful for the free-space quantum communication.