No-deleting principle for two unitary copies

Abstract

Pati and Braunstein defined a deleting machine and showed the impossibility of deleting one of two identical copies of an unknown quantum state. So far, no one has defined two non-identical copies of a quantum state, of course no one has discussed the impossibility of deleting one of two non-identical copies of an unknown quantum state. In this paper, we define $u|ψ>$ and $U|ψ>$, where $u$ and $U$ are any unitary operators, as two unitary copies of a quantum state $|ψ>$, and show that it is impossible to delete one of two unitary copies of an unknown state.