 After initially preparing the first and second qubits of the computer in the state \(\lvert 0\rangle\lvert 0\rangle\), one then “flips” the second qubit using a “NOT” gate (i.e. a Pauli X operation) to \(\lvert 1 \rangle\), and then subjects each qubit to a Hadamard gate. We now send the two qubits through an oracle or ‘black box’ which we imagine as a unitary gate, \(\mathbf{U}_f\), representative of the function whose character (of being either constant or balanced) we wish to determine. We define \(\mathbf{U}_f\) so that it takes inputs like \(\lvert x,y\rangle\) to \(\lvert x, y\oplus f (x)\rangle\), where \(\oplus\) is addition modulo two (i.e. exclusive-or). The first qubit is then fed into a further Hadamard gate, and the final output of the algorithm (prior to measurement) is the state: \[\pm\lvert f(0)\oplus f(1)\rangle~\lvert - \rangle,\] where \(\lvert - \rangle =_{df} \frac{| 0 \rangle - | 1 \rangle}{\sqrt 2}\). Since \(f\)(0)\(\oplus f\)(1) is 0 if the function is constant and 1 if the function is balanced, a single measurement of the first qubit suffices to retrieve the answer to our original question regarding the function’s nature. And since there are two possible constant functions and two possible balanced functions from \(f : \{0,1\} \rightarrow \{0,1\}\), we can characterise the algorithm as distinguishing, using only one oracle call, between two quantum disjunctions without finding out the truth values of the disjuncts themselves, i.e. without determining which balanced or which constant function \(f\) is (Bub 2010).