EXTRACTION OF VALUE OF FUNCTION f(x) IN DEUTSCH ALGORITHM AND DEUTSCH–JOZSA ALGORITHM

Deutsch algorithm or Deutsch–Jozsa algorithm only needs one query to determine whether the function f(x) is constant or balanced. That is, the global property of the function f(x) is rapidly known. But these algorithms do not give the concrete value of function f(x). For the f(x), its value is also of interest. Here we propose a scheme in which the value of function f(x) can be determined. We use an entangled state as the input state and send it into quantum black box. Through performing measurement on the output state, we can exactly determine the value of f(x). Its value plus its global property enables us to thoroughly understand elementary information of f(x). Based on these informations, we can determine unitary transformations on the input state walking through quantum black box. The quantum black box becomes quantum white box to a certain extent.