Probabilistic cloning and identification of linearly independent quantum states

Abstract

We construct a probabilistic quantum cloning machine by a general unitary-reduction operation. With a postselection of the measurement results, the machine yields faithful copies of the input states. It is shown that the states secretly chosen from a certain set $\$=\left\{|{\Psi }_1⟩,|{\Psi }_2⟩,...,|{\Psi }_n⟩\right\}$ can be probabilistically cloned if and only if , $|{\Psi }_2⟩$, $...,$ and $|{\Psi }_n⟩$ are linearly-independent. We derive the best possible cloning efficiencies. Probabilistic cloning has close connection with the problem of identification of a set of states, which is a type of $n+1$ outcome measurement on $n$ linearly independent states. The optimal efficiencies for this type of measurement are obtained.

Extension of quant-ph/9705018, 12pages, latex, to appear in Phys. Rev. Lett

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