 The situation is analogous for Deutsch’s function \(f\). Here the output of \(f\) can be represented as either \(\ket{0} \ket{0} + \ket{1} \ket{0}\) or \(\ket{0} \ket{1} + \ket{1} \ket{1}\) in the ‘constant’ case, or \(\ket{0} \ket{0} + \ket{1} \ket{1}\) or \(\ket{0} \ket{1} + \ket{1} \ket{0}\) in the ‘balanced’ case. The two entangled states in the ‘constant’ case are orthogonal in the 4-dimensional two-qubit state space and span a plane. Call this the ‘constant’ plane. Similarly, the two entangled states in the ‘balanced’ case span a plane, the ‘balanced’ plane. These two planes, representing two alternative quantum disjunctions, are orthogonal except for an intersection or overlap in a line, representing a product (non-entangled) state, where each qubit separately is in the state \(\ket{0} + \ket{1}\). It is therefore possible to design a measurement to distinguish the two alternative disjunctive or global properties of \(f\), ‘constant’ or ‘balanced,’ with a certain probability (actually, 1/2) of failure, when the measurement yields an outcome corresponding to the overlap state, which is common to the two cases. Nevertheless, only one query of the function is required when the measurement succeeds in identifying the global property. With a judicious choice of quantum gates, it is even possible to design a quantum circuit that always succeeds in distinguishing the two cases in one run.