  How to achieve an arbitrary real-valued probability amplitude in the general
single-partite or multipartite quantum system without measuring any other
quantum state's probability amplitude? How to achieve an arbitrary real-valued
probability amplitude with the deterministic polynomial time's complexity under
a small given error? In this paper, one novel quantum measurement scheme is
proposed to solve these questions based on the idea of binary searching. First,
the measurement algorithm with the exponential speed-up on the quantum state
with one single qubit is well-designed. Then, the measurement algorithm is
extended to the quantum states in the general multipartite quantum system and
the special multipartite quantum system. The theoretical analysis proves that
the proposed quantum measurement scheme has the performance in quantum
information processing with twofold advantages: separable measurement and
exponential speed up.
