Quantum Teleportation

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Introduction

Quantum teleportation is a protocol through which the state of a qubit can be transfered from Alice to Bob without the need to transmit the qubit through any medium. This feat is achieved with the use of a pre-existing entangled pair of qubits, one of which resides with Alice, while the other resides with Bob.

$$
\begin{align}
t_0 & = { p_0 } \\
t_1 & = { p_1 } \\
$ = { 2*p_0 (1+\alpha), p_0 (1-\alpha) } \\
t_2 & = { p_2 } \\
$ = 4*p_0 (1+\alpha)^2, 2*p_0 (1-\alpha^2), \\
& = 2*p_0 (1-\alpha^2), p_0 (1-\alpha)(1-{\frac {\alpha}{\theta}}) \\
t_3 & = { p_3 } \\
$ = 8*p_0 (1+\alpha)^3, 4*p_0 (1+\alpha)^2 (1-\alpha), \\
& = 2*p_0 (1-\alpha^2)(1+\alpha), 2*p_0 (1-\alpha^2)(1-{\frac {\alpha}{\theta}}), \\
& = 2*p_0 (1-\alpha^2)(1+\alpha), 2*p_0 (1-\alpha^2)(1-\alpha), \\
& = p_0 (1-\alpha)^2 (1+\alpha), p_0 (1-\alpha)(1-{\frac {\alpha}{\theta}})^2\\
\end{align}
$$