Chapter 5 Quantum entanglement

About the fundamental tool of quantum computing: entanglement, via the formalism of tensor products, which was the missing ingredient from our previous formalism of quantum theory. Also about various controlled gates, including the always useful controlled-\texttt{NOT}.

We now know everything we need to know about a single qubit and its quantum behaviour. But if we want to understand quantum computation — a complicated quantum interference of many interacting qubits — then we will need few more mathematical tools. Stepping up from one qubit to two or more is a bigger leap than you might expect. Already, with just two qubits, we will encounter the remarkable phenomenon of quantum entanglement and have a chance to discuss some of the most puzzling features of quantum theory that took people decades to understand.