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.

The essence of the issue for many, who seem to equate entanglement with FTL is that a classical channel is required. Without that, you’re just sending noise over your quantum channel.

Plus we get to keep cause and effect ordered, as a little bonus.