Is a single particle transition allowed between two superconductors having Majorana modes? Sorry maybe I ask a very naive and stupid question. The motivation to ask it is as follows:
I am considering the parity protection of Majorana qubit based on Kitaev's 1D model. As we know, in the Kitaev's chain model there are two free MFs on the end of the chain and the information in these two free MFs is protected by the parity of the superconductor substrate under the chains.
My question is as follows:

How about the parity protection if we consider a Kitaev junction (A nanowire hang on two superconductors and the middle of the nanowire is break up by a gate voltage)?
There are four MFs in the junction (from left to right named as 1,2,3,4), of course the combined parity of 12+34 is protected if we ignore the quasiparticle poisoning from environment, but how about the parity protection if we only consider 23?
Can 12 and 34 also have parity protection respectively?

 A: The answer is yes, a single electron can tunnel between two topological superconductors hosting unpaired Majorana modes.
Actually, since the Majorana pair flips (changes sign) by the injection of an electron inside the junction, a new term appears in the Josephson relation between two Majorana wires, which would be absent for a Josephson junction between two trivial superconductors. This is the famous $4\pi$-periodic Josephson Hamiltonian in the presence of some unpaired Majorana modes $\gamma_{L,R}$ on the left/right side of the junction, respectively, which reads 
$$H_{\text{M}}=\mathbf{i}E_{M}\gamma_{L} \gamma_{R} \cos\left(\dfrac{\varphi}{2}\right)$$
with $E_{M}$ the energy of the overlap of the Majorana modes from the different sides of the junction, and $\varphi$ the phase drop across the junction. The above term is relevant only at low energies and for short junctions, since at higher energy the usual Josephson term $H_{\text{J}}=E_{J}\left(1-\cos\varphi\right)$ dominates, whereas for long junctions the higher Andreev levels are more and more dense, and you'll no more see the signature of the zero-energy modes. 
$H_{\text{M}}$ term is particle-number conserved, since $\mathbf{i}\gamma_{L}\gamma_{R}\propto\hat{n}\pm1$. The proportionality factor is just a convention in the transformation between the $\gamma$'s and the usual creation and destruction operators $c^{\dagger}c=\hat{n}$ and it is of no importance here. If you add a particle-number conserved quantity, you keep the parity conservation of course, but you changed the relative parity conservation between the two wires separated by the junction, since $\gamma_{L}$ and $\gamma_{R}$ correspond to the unpaired Majorana modes on the left and on the right.
There is a huge literature about this effect, called fractional Josephson effect, $4\pi$-periodic Josephson current among others. I suggest you to read the pedagogical review


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*J. Alicea New directions in the pursuit of Majorana fermions in solid state systems. Reports on progress in physics, 75, 076501 (2012) -> available on arXiv:1202.1293 for free.


especially section V.B.
PS: Please comment if you need more details about your more specific questions. It is usually better to separate the questions, but yours are deeply correlated.
