## 3 A Detector-Blinding Attack on the BB84 with Passive Base Selection
She could, for example, in quite a realistic scenario, have been the vendor of [PERSON]'s station and could have measured the dark count rates (and all other relevant parameters) prior to selling it. While it was deemed in Ref. [4] that detector blindability is what makes the DBA viable, in this work, I go a step further and seek insight at the level of the information theory. First, I note that in order for the DBA to work, [PERSON] must make sure that her and [PERSON]'s detection bases match _before_ sending him a light signal that contains information. In the attack described above, the fake states contain the information [PERSON] wants [PERSON] to receive, while the continuous, circularly polarized blinding light does not contain any. Next, I note that a fake state pulse is split deterministically at the beam splitter (BS) such that exactly one-half of its power hits each detection base. This is in stark contrast with the BB84 in which [PERSON] receives a single qubit from [PERSON] and the BS serves as an internal and private entropy source which randomly selects one of [PERSON]'s two detection bases. Apparently, due to the deterministic splitting of a fake state under the DBA, the entropy of this internal randomness generator is zero--the entropy source is effectively disabled. But, without the random selection of bases, [PERSON] is unable to run the BB84 protocol. Whatever [PERSON] is actually running is _not_ the BB84, but he does not know this because he does not realize his entropy source has been compromised. In the BB84 protocol, the random base selection of the receiving station is a pivotal and indispensable facet of security. Let us investigate this in more detail. As explained above, as per the original BB84, [PERSON] must calculate his reception base in order to be able send this information to [PERSON]. He performs this based on his detections. Namely, if either the 0\({}^{\circ}\) or 90\({}^{\circ}\) detector fires, [PERSON] concludes that his random base is 0; if any the other two detectors fire, then the base is 1; and finally, if no detector fires or more than two detectors fire (e.g., due to noise), then the communication instance is inconclusive and must be discarded. If [PERSON] is monitoring the randomness of the sequence of bases (although this is not a part of the BB84 protocol), he would notice perfect randomness, but how could this occur when his own entropy source is incapacitated? Obviously, the randomness of his detection bases can be traced back to the beam splitter BS in the [PERSON] station, which is still functioning in the quantum regime because it is receiving single qubits from [PERSON]. This means that [PERSON] and [PERSON] are now logically united as one receiving station, \"Eve-Bob\", which carries out a correct BB84 protocol with [PERSON]. In effect, [PERSON] has sneaked into Bob (even though she might be physically far away) and is able to obtain enough information to arrive at the exact same key as [PERSON] and [PERSON]. What information does [PERSON] obtain? The DBA allows [PERSON] to directly set the detection outcome of any of the four detectors in [PERSON]; thus, she knows everything that [PERSON] knows. Indirectly, she also gains knowledge of [PERSON]'s bases. It is tempting to conjecture that if [PERSON] is monitoring the proper operation of his detectors, e.g., by making sure that they are not blinded and are sensitive to single photons, then devastating attacks like a DBA are impossible. However, could [PERSON] mount a successful attack without blinding the detectors? To answer this question, I consider two scenarios. In the first scenario, let us suppose that [PERSON] is able to set [PERSON]'s receiving base via some means other than detector blinding. Then, her best strategy would be to set [PERSON]'s base to match hers, but this time, she would send [PERSON] a single qubit matching her measurement. [PERSON] would detect the same bit as [PERSON] without any increased loss or error with respect to when [PERSON] is absent.