  We study the computational complexity of quantum-mechanical expectation
values of single-particle operators in bosonic and fermionic multi-particle
product states. Such expectation values appear, in particular, in
full-counting-statistics problems. Depending on the initial multi-particle
product state, the expectation values may be either easy to compute (the
required number of operations scales polynomially with the particle number) or
hard to compute (at least as hard as a permanent of a matrix). However, if we
only consider full counting statistics in a finite number of final
single-particle states, then the full-counting-statistics generating function
becomes easy to compute in all the analyzed cases. We prove the latter
statement for the general case of the fermionic product state and for the
single-boson product state (the same as used in the boson-sampling proposal).
This result may be relevant for using multi-particle product states as a
resource for quantum computing.
