Probabilistic deletion of copies of linearly independent quantum states
Jian Feng, Gao Yun-feng, Ji‐Suo Wang, Mingsheng Zhan · Physical Review A · 2002
We show that each of two copies of the nonorthogonal states randomly selected from a certain set S can be probabilistically deleted by a general unitary-reduction operation if and only if the states are linearly independent. We derive a tight bound on the best possible deleting efficiencies. These results for $\stackrel{\ensuremath{\rightarrow}}{2}1$ probabilistic deleting are also generalized into the case of $\stackrel{\ensuremath{\rightarrow}}{N}M$ deleting (N,M positive integers and $N>M).$