Rigorous security proof for Wiesner's quantum money?
It seems like this interaction can be modeled in the following way:


Alice prepares one of the states $|000\rangle$, $|101\rangle$,$(|0\rangle+|1\rangle)|10\rangle/\sqrt{2}$, $(|0\rangle-|1\rangle)|11\rangle/\sqrt{2}$, according to a certain probability distribution, and sends the first qubit to Bob.
Bob performs an arbitrary quantum channel that sends his qubit to two qubits, which are then returned to Alice.
Alice performs a projective measurement on the four qubit on her possession. 


If I am not wrong about this (and sorry if I am), this falls within the formalism from Gutoski and Watrous presented here and here, which implies that:


From Theorem 4.9 in the second of those, it is optimal to Bob to act independently  when Alice repeats this process with several qubits in an independent way, if the objective of Bob is to always fool Alice.
It is possible to obtain the value of c from a small semidefinite program. You can find more details of how to obtain this program in Section 3 here. See the comments for the cvx code for the program and its value.