PROBABILISTIC CLONING AND IDENTIFICATION OF LINEARLY INDEPENDENT QUANTUM STATES

We construct a probabilistic quantum cloning machine by a general unit ary-reduction operation. With a postselection of the measurement resul ts, the machine yields faithful copies of the input states. It is show n that the states secretly chosen from a certain set S = {\Psi(1)], \P si(2)],...,\Psi(n)]} can be probabilistically cloned if and only if \P si(1)], \Psi(2)],..., and [Psi(n)] are linearly independent. We derive the best possible cloning efficiencies. Probabilistic cloning has a c lose connection with the problem of identification of a set of states, which is a type of n + 1 outcome measurement on n linearly independen t states. The optimal efficiencies for this type of measurement are ob tained.