De-quantization and Entanglement

The Deustch-Jozsa problem is one of the most basic ways to demonstrate the power of quantum computation. Consider a Boolean function f : {0, 1} → {0, 1} and suppose we have a black-box to compute f . The Deutsch-Jozsa problem is to determine if f is constant (i.e. f(x) = const, ∀x ∈ {0, 1}) or if f is balanced (i.e. f(x) = 0 for exactly half the possible input strings x ∈ {0, 1}) using as few calls to the black-box computing f as is possible, assuming f is guaranteed to be constant or balanced. Classically it appears that this requires at least 2n−1 + 1 black-box calls in the worst case, but the well known quantum solution solves the problem with probability one in exactly one black-box call. It has been found that in some cases the algorithm can be de-quantised into an equivalent classical, deterministic solution. We explore the ability to extend this de-quantisation to further cases, and examine with more detail when de-quantisation is possible, both with respect to the Deutsch-Jozsa problem, as well as in more general cases.