While the image is correct, your statement would be a bit misleading to novices: You can not transfer the state of the qubit over a classical channel. You need

While the image is correct, your statement would be a bit misleading to novices: You can not transfer the state of the qubit over a classical channel. You need both a classical channel and entanglement. Or in other words: a bit can be send over a classical communication channel (by copying it), but to transmit a qubit (which can not be copied due to its quantum nature), you either need to carry the physical qubit over, or use entanglement together with classical communication.