  Using tools from quantum information theory, we present a general theory of
indistinguishability of identical bosons in experiments consisting of passive
linear optics followed by particle number detection. Our results do neither
rely on additional assumptions on the input state of the interferometer, such
as, for instance, a fixed mode occupation, nor on any assumption on the degrees
of freedom that potentially make the particles distinguishable. We identify the
expectation value of the projector onto the $N$-particle symmetric subspace as
an operationally meaningful measure of indistinguishability, and derive tight
lower bounds on it that can be efficiently measured in experiments. Moreover,
we present a consistent definition of perfect distinguishability and
characterize the corresponding set of states. In particular, we show that these
states are diagonal in the computational basis up to a permutationally
invariant unitary. Moreover, we find that convex combinations of states that
describe partially distinguishable and perfectly indistinguishable particles
can lead to perfect distinguishability, which itself is not preserved under
convex combinations.
