 Deutsch (1989) asks the following question: Suppose we have a function \(f\) which can be either constant—i.e. such that it produces the same output value for each of its possible inputs, or balanced—i.e. such that the output of one half of its possible inputs is the opposite of the output of the other half. The particular example considered is the function \(f : \{0,1\} \rightarrow \{0,1\}\), which is constant if \(f\)(0) \(= f\)(1) and balanced if \(f\)(0) \(\ne f\)(1). Classically it would take two evaluations of the function to tell whether it is one or the other. Quantumly, we can answer this question in one evaluation. For Deutsch, the explanation for this complexity reduction involves an appeal to “many computational worlds” (see section 5.1.1).  Arguably, however, a fully satisfactory answer appeals only to the superposition principle and entanglement (Bub 2010).