Quantum teleportation is an overhyped idea with no practical application. The main use is supposed to be Quantum key distribution:
Quantum key distribution (QKD) uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages. It is often incorrectly called quantum cryptography, as it is the most well known example of the group of quantum cryptographic tasks.Transmitting a message securely means that the recipient gets a message that could have only come from the sender, and no eavesdropper can read or interfere with the message. Conventional cryptography solves this problem. The QKD method has no way to autheniticate the sender, and can never be secure. At best it has a statistical method for probably detecting eavesdroppers.
An important and unique property of quantum distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states, a communication system can be implemented which detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e. the eavesdropper has no information about), otherwise no secure key is possible and communication is aborted.
A physics blog explains quantum teleportation. That allows someone to send a quantum bit (qubit) to another.
If individual photons had mathematical representations, then they could be teleported by just transmitting those numbers and reconstructing the photon state at the other end. Without such representations, the so-called teleportation is a little trickier, but not big deal. I think someone else will get the Nobel prize.