Many protocols and experiments in quantum information science are described in terms of simple measurements on qubits. However, in an experimental implementation, the exact description of the measurement is usually more complicated. If there is a claim made from the results of an experiment by using the simplified measurement description, then do the claims still hold when the more realistic description is taken into account? We present a "squashing" model that decomposes the realistic measurement description into first a map, followed by a simplified measurement. The squashing model then provides a connection between a realistic measurement and an ideal measurement. If the squashing model exists for a given measurement, then all claims made about a measurement using the simplified description also apply to the complicated one. We give necessary and sufficient conditions to determine when this model exists. We show how it can be applied to quantum key distribution, entanglement verification, and other quantum communication protocols. We also consider several examples of detectors commonly used in quantum communication to determine if they have squashing models.iii

Quantum key distribution protocols typically make use of a one-way quantum channel to distribute a shared secret string to two distant users. However, protocols exploiting a two-way quantum channel have been proposed as an alternative route to the same goal, with the potential advantage of outperforming one-way protocols. Here we provide a strategy to prove security for two-way quantum key distribution protocols against the most general quantum attack possible by an eavesdropper. We utilize an entropic uncertainty relation, and only a few assumptions need to be made about the devices used in the protocol. We also show that a two-way protocol can outperform comparable one-way protocols

We develop a framework that allows a description of measurements in Hilbert spaces that are smaller than their natural representation. This description, which we call a "squashing model", consists of a squashing map that maps the input states of the measurement from the original Hilbert space to the smaller one, followed by a targeted prescribed measurement on the smaller Hilbert space. This framework has applications in quantum key distribution, but also in other cryptographic tasks, as it greatly simplifies the theoretical analysis under adversarial conditions.

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 multiphoton events can be neglected