= Perfect quantum state transfer
{title2=$e^{-iHt_*}|a\rangle=e^{i\chi}|b\rangle$}
A <Hamiltonian operator> has perfect transfer between <basis> states $|a\rangle,|b\rangle$ at time $t_*$ if $e^{-iHt_*}|a\rangle=e^{i\chi}|b\rangle$ for a known <global phase> $\chi$. In an excitation-conserving <qubit> network whose vacuum is fixed, the initial <product state> with $\alpha|0\rangle+\beta|1\rangle$ at site $a$ and zeros elsewhere evolves to $\alpha|\mathrm{vac}\rangle+\beta e^{i\chi}|b\rangle$. A local <phase gate> at $b$ removing $\chi$ restores the unknown <qubit> there. This explains why transfer of the single-excitation <basis> state suffices for <qubit> transfer when the vacuum phase is also accounted for.
Back to article page
