An algebraic approach to quantum information theory with applications in quantum cryptography

We present an algebraic approach to quantum information theory and its application to quantum cryptography. Therefore, we model the measurement process in terms of an algebraic object: a partition of unity. The POVM associated to such a partition describes the measurement results and the completely positive map associated to it the disturbance of the state. This approach leads to a compact description of quantum cryptography in which general measurements, noisy channels as well as measurement apparatus of the receiver that are out of sync with those of the sender can be described.