Minimum-energy pulses for quantum logic cannot be shared
Julio R. Gea-Banacloche, Masanao Ozawa · Physical Review A · 2006
We show that if an electromagnetic energy pulse in a multimode coherent state with average photon number $\overline{n}$ is used to carry out the same quantum logical operation on a set of $N$ atoms, either simultaneously or sequentially, the overall error probability in the worst-case scenario (i.e., maximized over all the possible initial atomic states) scales as ${N}^{2}∕\overline{n}$. This means that in order to keep the error probability bounded by $Nϵ$, with $ϵ\ensuremath{\sim}1∕\overline{n}$, one needs to use $N\overline{n}$ photons or, equivalently, $N$ separate ``minimum-energy'' pulses: in this sense the pulses cannot, in general, be shared. The origin of this phenomenon is found in atom-field entanglement. These results may have important consequences for quantum logic and, in particular, for large-scale quantum computation.