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}