## motivating entanglement

file:///Users/houliu/Documents/School Work/The Bible/Quantum/Leonard Susskind, Art Friedman - Quantum Mechanics_ The Theoretical Minimum-Basic Books (2014).pdf

Take two actors, Alice \(A\) and Bob \(B\). They each have a space \(S_A\) and \(S_B\). What if, for instance, we want to create a composite system out of Alice and Bob?

We will define elements in the Alice space as being defined by bases \(H\) and \(T\), where each element \(a \in S_a\) is defined as:

\begin{equation} \alpha_H | H \big\} + \alpha_T | T \big\} \end{equation}

Why the weird kets? We will use different kets to be aware of where bases came from; as in, elements in Alicespace is not elements in Bobspace.

Let’s take Bobspace to be a higher dimension, as in, using normal ket vectors:

\begin{align} |1\big> \\ |2\big> \\ |3\big> \\ \cdots \\ |6\big> \end{align}