of the Fuchs-Peres-Brandt attack. We recognize, of course, that the decision to use active basis selection is Bob’s to make, not Eve’s. More importantly, however, in Sec. IV we will show how the availability of polarization-preserving QND photon-number measurements can be used to turn Fig. 6 into a true, deterministic implementation of the FPB attack. The same conversion can be accomplished for passive basis selection. Before turning to the true-attack implementation, let us flesh out some details of the measurement box in Fig. 6 and show how SPDC can be used, in lieu of the single-photon source, to perform this physical simulation.

Let $|\psi_{\rm out}\rangle$ denote the polarization$\otimes$momentum state at the output of Eve’s P-CNOT gate in Fig. 6. Bob’s polarization analysis box splits this state, according to the basis he has chosen, so that one basis state goes to the upper branch of the measurement box while the other goes to the lower branch of that box. This polarization sorting does nothing to the momentum qubit, so the SWAP gates, half-wave plates, and polarizing beam splitters that Eve has inserted into the measurement box accomplish her $\{|d_+\rangle, |d_-\rangle\}$ projective measurement, i.e., the horizontal paths into photodetectors in Fig. 6 