Orthogonality of Two-State Vectors

Now that we have developed a basic understanding of a quantum state vector, let’s look at a few simple mathematical techniques that will be useful in understanding quantum computation. Many operations in QC involve multiplying two state vectors together to obtain a number (called a scalar), rather than another vector. A “scalar” is just a regular number with no direction associated with it. This kind of product is often called a scalar product or an inner product, or a dot product since the dot product notation $\vec{C}\cdot\vec{B}$ is often used in standard vector algebra. The following figure shows two vectors and their components in state space.