A set of quantum states can be virtually cloned if and only if their density matrices are linearly independent, and the optimal 1-to-2 cloning cost for any pair of pure states equals sqrt(1+|⟨ψ1|ψ2⟩|²).
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Virtual Cloning of Quantum States
A set of quantum states can be virtually cloned if and only if their density matrices are linearly independent, and the optimal 1-to-2 cloning cost for any pair of pure states equals sqrt(1+|⟨ψ1|ψ2⟩|²).