Quantumness: In order to identify quantum features, in contrast to classical systems, we study various representations of quantum states, such as Wigner functions and their discrete analogues, or the multipole representation of polarization of multiphoton states.
Tomography: An important task in quantum mechanics is to estimate the state of a quantum system based on measurement results. We study tomographically complete sets of measurements and their structure, including MUBs and SICPOVMs. When the system gets larger, complete tomography becomes infeasible and hence quantum states have to be estimated based on incomplete measurements.
Entanglement: Unlike classical systems, the state space of a composite quantum systems grows exponentially with the number of component systems. Almost all states in a composite quantum system are entangled, but the characterization of different types of multipartite entanglement is still not well understood. We use algebraic tools to identify and describe different types of entanglement.
Codes: Quantum states are very sensitive to interaction with the environment, but at the same time quantum mechanics allows mechanism to protect quantum information when suitably encoded in subspaces of the system. We study bounds on the parameters of codes, including constructions establishing lower bounds and codes for specific physically relevant channels, like amplitude damping. Furthermore, we consider the problem of optimal discrimination of quantum states, which has, e.g., applications when classical information is transmitted.
