# Quantum Teleportation

The goal of teleportation is to transfer the unknown state information of the source (first) qubit without measuring or observing, to the destination (second) qubit. Thereby avoiding the disturbance of the first [1, 2, 4]. The second qubit, therefore, doesn’t receive a copy of the quantum state of the first since it is impossible to produce an exact copy of an arbitrary quantum state that is called **No-cloning theorem**.

As it turns out, the second qubit doesn’t need a copy of the state information of the first – the original state of the first is teleported to it. Note that the process isn’t faster than light and a pair of entangled states has to be distributed ahead of time:

1. At the start, assume a single-qubit state.

| Ψ> = α|0>+β|1>

at location A, and that α and β in the state are unknown. Therefore, the unnecessary information to specify the state at location A is not available.

2. Generate an entangled state of a pair of qubits, assume the entangled state is a Bell (EPR) state and is written as:

|v>=(1/√2)(|00>+|11>)

3. To teleport the qubit from location A to location B, create a tensor product of the qubit of at A with v.

4. Next the two qubits in location A are sent through a CNOT gate. A CNOT gate inverts the state of the second qubit if the first qubit is in state 1, otherwise, nothing changes. Thus, the second qubit of terms 3 and 4 in the state w_{0} gives a new state.

5. Next Qubit 1, which is the first qubit that initially contains the state to be teleported. It is sent through a Hadamard gate. There are four terms in state w_{1} with the first qubit being in state 0, 0, 1 and 1 respectively. As indicated previously a Hadamard gate transforms state |0> and |1> into

|0>= (1/√2)(|0>+|1>)

|1>= (1/√2)(|0>-|1>)

respectively.