in this paper the authors describe in equation 33 a generic way to compute the inner product between DSN states and then in the appendix in equation A5 a compact form between two displaced squeezed states as shown in the fig below:
when i try to implement this equation using straightforward numpy, the squeezing part is working perfectly as it should be and also as mentioned in your paper. The displacement part is also correct and it matches what strawberryfields produces. “calculating the inner product between two displaced states or two squeezed states”.
However, the inner product between two DS states doesn’t match the output from equation A5 and the output from strawberryfields is much more realistic in terms of separability. for example r_1 = 1, \ \ r_2=0.-2, \\ d_1=0.4,\ \ d_2=-0.4
the term |<\psi_1|\psi_2>|^2 is very low using both of the fock backend and gaussian backend. but it doesn’t match the output from equation A5.