## 3 Bell State Exchange Parity Protocol and Intrinsic Autocompensation  
The analysis performed in the above section shows, through the BBM92 protocol, that QKD based on Bell states, that is, entangled states, presents severe problems when it comes to autocompensation. That is, plug and play based on a single back-forth round trip cannot be used. In order to avoid this drawback, we propose a protocol (see Figure 2) based on Bell state exchange parity (BSEP), conceptually similar to some theoretical QKD idealizations [31]. In our case, we put it in concrete terms, allowing for full intrinsic autocompensation. We must stress that this proposed plug and play protocol with a single round trip is for biphoton entangled states and it also uses three subsystems Charlie-Alice/Bob, which avoids attacks on the photodetection subsystem. In other words, it contains all the advantages of the MDI-QKD protocol. Accordingly, it is fully different from those based on single-photon states [13; 14; 21] with only two subsystems (Alice/Bob) which are therefore defenseless to attacks on the photodetection subsystem. The physical system implements a protocol with a built-in autocompensation mechanism. In particular, we make use of the states \(|\Psi^{+}\rangle\) and \(|\Psi^{-}\rangle\), which can be measured with linear optics. Each encoding requires specific hardware, but they all are conceptually similar. In the case of polarization, we directly use the Innsbruck-type scheme [32], that is, PBSs. Next, we adapt it to the other encodings, as shown in Figure 3. For the case of codirectional modes, Bell state measurements can be performed by means of a small integrated optical circuit, that is, by using two 3 dB directional couplers. For collinear modes, the setup is that of polarization, but polarizing beam splitters are substituted with mode-sorting Mach-Zehnder Interferometers (MZIs), which are regular MZIs but with an unrotated Dove prism in one arm (DP\({}_{0}\)), that is, with its normal forming an angle equal to 0 with respect to direction \(Y\). Therefore, a phase retarder \(\pi\) is produced and consequently, a \(Z\) transformation is implemented.  
We shall collectively refer to any of these Bell state analyzers as a Bell measurement device (BMD). Photons are bosons, so their overall wavefunction needs to be symmetric. This means that they emerge on different paths at the output of the BMD if they are in any of the (triplet) Bell states or come out in different paths if they are in the singlet state. In practice, this discriminates one Bell state from the others [33]. In other words, Bell state exchange parity produces distinguishable outcomes, and these outcomes can be used to generate a key.  
Figure 2: Bell state exchange parity protocol. Both the source and the BMD are situated in the middle. From there, fiber links extend up to [PERSON] and [PERSON]’s stations, where phase modulation is performed and autocompensation transformations are applied, which also communicate through a classical channel. Arrows indicate a round trip, and two pulses in each path indicate a temporal superposition state for a single photon (see Section 3.2). The structure and principle of the protocol are common to all three encodings.