Matrix analysis
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We present a scheme of quantum information transmission, which transmits the quantum information contained in a single qubit via the quantum correlation shared by two parties (a two-qubit channel), whose quantum discord is non-zero. We demonstrate that quantum correlation, which may have no entanglement, is sufficient to transmit the information needed to reconstruct a quantum state. When the correlation matrix of the two-qubit channel is of full rank (rank three), the information of the qubit (in either a mixed state or a pure state) can be transmitted. The quantum discord of a channel with rank larger than or equal to three is always non-zero. Therefore, non-zero quantum discord is also necessary for our quantum information transmission protocol. The scheme may be useful in remote state tomography and remote state preparation.