8.2 Entanglement
We’ve now seen many gate operations that you can apply to a single qubit to change its state. In section 2.5
While we can apply not to a single bit, all the other operations require at least two bits for input. In the same way, we need to work with multiple qubits to produce interesting and useful results.
8.2.1 Moving from one to two qubits
As discussed above, the states of a single qubit are represented by vectors of length 1 in C2 and all such states that differ only by multiplication by a complex unit are considered equivalent. Each qubit starts by having its own associated copy of C2.
When we have a quantum system with two qubits, we do not consider their collective states in a single C2 instance. Instead, we use the tensor product of the two copies of C2 and the tensor products of the quantum state vectors. This gives us a four-dimensional complex vector space where this ‘‘4’’ is 2 × 2 rather...
