The power of information theory – classical as well as quantum – originates in the abstraction of information from its physical carrier. On this level of discussion, every process, every time evolution and every operation is described by a quantum channel – an input-output relation abstracting from the microscopic origin of the physical dynamics. Quantum channels are therefore central objects and basic building blocks in quantum information theory. The composition of quantum channels is a very natural operation arising in most physical situations. Sequential composition arises, for instance, when two quantum processes are carried out one after the other. It is therefore surprising that a systematic study is still missing that analyses the effect of composition on basic properties of quantum channels, such as the ability to reliably transmit quantum information.
With this project we propose to fill this gap and provide a first in-depth analysis of fundamental properties of quantum channels, with a particular emphasis on the behaviour under sequential and parallel composition. We will, furthermore, initiate the study of complexity-theoretic properties of quantum channels, thereby providing a novel computer science perspective on quantum channels.
We expect the results from this project to have a profound impact to the study of quantum spin chains, quantum complexity theory and quantum cryptography. The project as well as the consortium is of interdisciplinary nature and will use modern tools from operator space theory, signal processing, convex geometry and complexity theory.
