Recursive calculation of threshold probabilitites

[nquesada]

It would be good to find a way to calculate recursively all the click probabilities of a Gaussian state.

[ziofil]

oh man I've been thinking about this about a year ago. The issue was that the diagonal elements are linear combos of off-diagonal ones, so in order to traverse the density matrix tensor on the diagonals we need off-diagonal values too.

maybe we can do it for pure states though by combining two recurrence relations (one for the amplitudes and one for the conjugate of the amplitudes)

[nquesada]

I think you are thinking about photon-number probabilities, I am mostly thinking about click probabilities.

[ziofil]

Oh I see, you want the vacuum marginals essentially...
is there a way of computing a marginal by acting somehow on the generating function?

Oh wait it's a Gaussian state. It's trivial to compute marginals. uhm.... 🤨

[jakeffbulmer]

This is on my todo list (also including internal modes), but if any progress is being made in this direction, let me know!