  The transmission of photons through open-air or an optical fiber is an
important primitive in quantum information processing. Theoretical description
of such a transmission process often considers only a single photon as the
information carrier and thus fails to accurately describe experimental optical
implementations where any number of photons may enter a detector. It is
important to bridge this big gap between experimental implementations and the
theoretical description. One powerful method that emerges from recent efforts
to achieve this goal is to consider a squash model that conceptually converts
multi-photon states to single-photon states, thereby justifying the equivalence
between theory and experiments. However, up to now, only a limited number of
protocols admit a squash model; furthermore, a no-go theorem has been proven
which appears to rule out the existence of a universal squash model. Here, we
observe that an apparently necessary condition demanded by all existing squash
models to preserve measurement statistics is too stringent a requirement for
many protocols. By chopping this requirement, we show that rather surprisingly,
a universal squash model actually exists for a wide range of protocols
including quantum key distribution protocols, quantum state tomography, the
testing of Bell's inequalities, and entanglement verification, despite the
standard no-go theorem.

Quantum Physics