Phase Kickback

Quantum entanglement is one of the astonishing characteristics of quantum mechanics. Two entangled particles share a state of superposition no matter how far apart they are.

From a practical perspective, we can use entanglement to let one qubit control the state of another. For instance, the controlled NOT-gate (CNOT- or CX-gate) switches the amplitudes of a target qubit only if the control qubit is in state $|1\rangle$. Nothing happens if the control qubit is in state $|0\rangle$.

Such controlled quantum gates let us precisely manipulate a multi-qubit system. In the lesson Composing Quantum Computing Controls, we let certain states of the quantum system exhibit the measurement probabilities we want them to have. We use entanglement to create a fine-grained probabilistic system.

Another practical characteristic of controlled quantum gates is that they leave the control qubit untouched.

The following figure depicts the truth table of the CNOT-gate.