entering the polarizing beam splitter that follows the half-wave plate. This beam splitter routes these polarizations into its transmitted and reflected output ports, respectively, where, in each arm, Eve employs a SWAP gate, a polarization-preserving QND measurement of total photon number, and another SWAP gate. The first of these SWAPs returns Alice’s BB84 qubit to polarization, so that a click on Eve’s polarization-preserving QND apparatus completes her $\{|d_+\rangle, |d_-\rangle\}$ measurement without further scrambling Alice’s BB84 qubit beyond what has already occurred in Eve’s P-CNOT gate. The SWAP gates that follow the QND boxes then restore definite ($V$ and $H$) polarizations to the light in the upper and lower branches so that they may be recombined on a polarizing beam splitter. The SWAP gate that follows this recombination then returns the BB84 qubit riding on Alice’s photon to polarization for transmission to and measurement by Bob. This photon is no longer in the single spatial mode emitted by Alice’s transmitter, hence Bob could use spatial-mode discrimination to infer the presence of Eve, regardless of the $P_E$ value she had chosen to impose. Eve, however, can preclude that possibility. Because the result of her $\{|d_+\rangle,|d_-\rangle\}$ measurement tells her the value of the 