1 postdoc and 3 PhD student positions are available in this project. We offer good salaries and possibility to work on a wide range of topics. To apply send your CV and a short description of scientific interests to email@example.com Any inquires should be directed to the same address.
Study of quantum information processing in the case when communication and memory are limited to just a few qubits. We are interested in doing this mainly in the context of the three following fileds:
Foundations: We expect that our studies will, first of all, improve our understanding of the foundations of the quantum theory. We will work on memory cost of contextuality, various aspects
of temporal Bell inequalities and statistical complexity of the systems required to describe experimental results.
Quantum information: On the information processing side we will design and analyze novel quantum communication protocols. We will concentrate our studies on following tasks: (a) nonclassicality
indicators - which, if a certain efficiency is reached, imply that quantum resources have been used; (b) dimension witnesses - which provide lower bounds on the size of the message; (c) random access codes - which provide a lossy way of data compression in such a way that the receiver is able to choose, to a certain extent, which part of information is lost. For all these cases we will analyze their efficiency, robustness to noise and imperfect detectors. Later we will study their
generalization to communication networks with many senders, receivers and relays. Moreover, we will consider their usefulness for cryptography and random number generation. Finally, we will collaborate with experimental groups to test our protocols in their laboratories.
Communication complexity: The third area of research covered in the project is classical communication complexity. Results in the foundations part will mostly be based on comparison between classical and quantum efficiencies for certain tasks. Therefore, the first goal here is to rephrase the communication tasks from the quantum information part as communication complexity problems and find the optimal efficiency of their classical counterparts. It will also naturally introduce scenarios
not considered so far in classical communication theory. For example, to make the comparison full, we will have to study how protocol’s efficiency depends on detector performance. We will concentrate our work on the case when the communication allowed is severely limited which also hasn’t been studied as much as the asymptotic case. Apart from opening a new area of research linking the foundations to communication complexity will enable us to use the powerful mathematical apparatus of the latter in the former.