Many protocols and experiments in quantum information science are described
in terms of simple measurements on qubits. However, in a real implementation,
the exact description is more difficult, and more complicated observables are
used. The question arises whether a claim of entanglement in the simplified
description still holds, if the difference between the realistic and simplified
models is taken into account. We show that a positive entanglement statement
remains valid if a certain positive linear map connecting the two
descriptions--a so-called squashing operation--exists; then lower bounds on the
amount of entanglement are also possible. We apply our results to polarization
measurements of photons using only threshold detectors, and derive procedures
under which multi-photon events can be neglected.Comment: 12 pages, 2 figure
