Summary

When combined with other gates, a two-qubit CNOT gate can entangle qubits. An entangled pair behaves as a single unit in which the measurement of one qubit determines the outcome of measuring the other. Neither qubit exists independently in a state of its own. The two-qubit system cannot be represented as the tensor product of two single qubits.

The true nature of entanglement remains a mystery for physicists. Experiments indicate that the theory has no hidden variables, so the qubits don’t know if they’ll be 0s or 1s before they’re measured. But at the time of each measurement, the qubits may be separated by many light-years. And yet, news of one qubit’s measurement seems to travel instantaneously to inform the other qubit’s measurement. No one knows exactly why this happens. As physicist Richard Feynman said, the best we can do is to “Shut up and calculate”.

In this chapter, we leveraged the fact that you can’t...