Introduction to Cryptography with Coding Theory, 3rd Edition

25.2 Quantum Key Distribution

Now that we have set up some of the ideas behind quantum mechanics, we can use them to describe a technique for distributing bits through a quantum channel. These bits can be used to establish a key that can be used for communicating across a classical channel, or any other shared secret.

We begin by describing a quantum bit. Start with a two-dimensional complex vector space. Choose a pair of orthogonal vectors of length 1; call them $|0⟩$ and $|1⟩$. For example, these two vectors could be either of the two pairs of orthogonal vectors used in the previous section. A quantum bit, also known as a qubit, is a unit vector in this vector space. For the purposes of the present discussion, we can think of a qubit as a polarized ...