We investigate the probabilistic quantum cloning (PQC) of two states with arbitrary probability distribution. The optimal success probabilities are worked out for $$1\rightarrow 2$$ 1 → 2 PQC of the two states. The results show that the upper bound on the success probabilities of PQC in Qiu (J Phys A 35:6931–6937, 2002) cannot be reached in general. With the optimal success probabilities, we design simple forms of $$1\rightarrow 2$$ 1 → 2 PQC and work out the unitary transformation needed in the PQC processes. The optimal success probabilities for $$1\rightarrow 2$$ 1 → 2 PQC are also generalized to the $$M\rightarrow N$$ M → N PQC case.
Quantum Information Processing – Springer Journals
Published: Dec 10, 2015
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