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Three-or-more-photon pulses

When the number of photons is three or more, it is possible to determine the state of the pulse uniquely, with a probability strictly smaller than 1 [10]. For simplicity, we will be generous to Eve, and assume that she can determine the state of every three-or-more photon pulse precisely. She can then forward a strong pulse in the right state to Bob. Since this gives Eve full information at the cost of no errors at Bob's side, it is evident that Eve should do this for every such pulse.

As we have seen, the probability that Alice sends such a pulse is at most $\lambda ^3/6$. The fraction of sent pulses that are detected is $\lambda F \eta_B$, so by the same argument as for the SO attack, such pulses can contribute at most a fraction

\begin{displaymath}f_3:= \frac{\lambda ^3}{6\lambda F \eta_B} = \frac{\lambda ^2}{6 F \eta_B}\end{displaymath}

to the bits in the raw key.

Louis Salvail 2001-06-15