Editing Qubit (section)

===Controlled gate to construct the Bell state===
[[Quantum logic gate#Controlled gates|Controlled gates]] act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the [[controlled NOT gate]] (CNOT or CX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is <math>|1\rangle</math>, and otherwise leaves it unchanged. With respect to the unentangled product basis <math>\{|00\rangle</math>, <math>|01\rangle</math>, <math>|10\rangle</math>, <math>|11\rangle\}</math>, it maps the basis states as follows:
:<math> | 0 0 \rangle \mapsto | 0 0 \rangle </math>
:<math> | 0 1 \rangle \mapsto | 0 1 \rangle </math>
:<math> | 1 0 \rangle \mapsto | 1 1 \rangle </math>
:<math> | 1 1 \rangle \mapsto | 1 0 \rangle </math>.

A common application of the CNOT gate is to maximally entangle two qubits into the <math>|\Phi^+\rangle</math> [[Bell state]]. To construct <math>|\Phi^+\rangle</math>, the inputs A (control) and B (target) to the CNOT gate are:

<math>\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)_A</math> <math>\otimes</math> <math>|0\rangle_B</math> = <math>\frac{1}{\sqrt{2}}</math> <math>(|00\rangle + |10\rangle)</math>.

After applying CNOT, the output is the <math>|\Phi^+\rangle</math> Bell State: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>.