Suppose that we have two entangled states $\ket { \phi_1}$, $\ket{ \psi_1}$ that cannot be converted to any of other two states $\ket{ \phi_2}$, $\ket{ \psi_2}$ by local operations and classical communication. We analyze the possibility of locally transforming a superposition of $\ket{ \phi_1}$ and $\ket{ \psi_1}$ into a superposition of $\ket{ \phi_2}$ and $\ket{ \psi_2}$. By using the Nielsen's theorem we find the necessary and sufficient conditions for this conversion to be performed.
Categories: quant-ph