I am reading a paper "A study of Teleportation and Super Dense Coding capacity in Remote Entangled Distribution" (arXiv:1210.1312). In this paper Relations on two-qubit pure states are mentioned.
Consider a resource entangled in 2 $\otimes $ 2 dimensions. These states are given by
$| {\psi_{12}} \rangle $ = $\sum_{i, j}a_{ij} |ij \rangle $ and
$| {\psi_{23}} \rangle $ = $\sum_{p, q}b_{pq} |pq \rangle $
where $\sum_{i, j}a_{ij}^2 = 1 $, $\sum_{p, q}b_{pq}^2 = 1 $
Alice and Bob share a pure entangled state $| {\psi_{12}} \rangle $ between them, Bob and Charlie also share another entangled state $| {\psi_{23}} \rangle $.
In order to swap the entanglement, Bob carries out measurement on his qubits. Bob carries out measurement for his two qubits in a non-maximally Bell-type entangled basis given by the basis vectors
$| \phi_{G}^{rh} \rangle $ = $\frac{1}{\sqrt{B_{rh}}} (\sum_{t =0}^{1}e^{I\pi rtR_{t}^{rh}}|t\rangle|t\oplus h\rangle) $
Now according to general measurements done by Bob on his qubits, we have four possible states between Alice and Charlie’s locations respectively. These four possible states based on Bob’s measurement outcomes are
$|\chi^{rh} \rangle$ = $\frac{1}{\sqrt{M_{rh}}} \sum_{i, q=0}^1 (\sum_{j=0}^1 e^{-I\pi rj}R^{rh}_{j}a_{ij}b_{j\oplus h, q})|iq\rangle$
where
$M_{rh}$ = $\sum_{i, q=0}^1 (\sum_{j=0}^1 e^{-I\pi rj}R^{rh}_{j}a_{ij}b_{j\oplus h, q})^2$
I was unable to understand how ℎ resolves to a value when I take (r, h) as (0, 0)?
