Abstracts

Dr. Nilanjana Datta
Entropies and Majorization in Quantum Information Theory​

Entropies play a key role in Quantum Information Theory. The von Neumann entropy characterizes the optimal rate of quantum data compression. It also arises as the characteristic quantity in the important operational tasks of entanglement distillation and entanglement dilution. The von Neumann entropy belongs to a larger class of entropies, called Renyi entropies, which too have important operational significance, for example, in state discrimination. In these lectures we will study a fundamental property of these entropies, namely, continuity.
This concerns the following question: “If two quantum states are close to each other, how close are their entropies?”
To address this question, we employ a powerful mathematical toolkit, called Majorization Theory.
Then we use our results to study the interesting problem of conversion of bipartite states, shared between two distant parties, via local operations and classical communication (LOCC).

Prof. Jonathan Oppenheim
Quantum resource theories and quantum thermodynamics

These lectures will provide a tutorial on the general structure of quantum resource theories and their application to quantum thermodynamics. Topics covered may include: the Szilard engine, Maxwell’s demon, resource monotones, majorisation theory, and the many second laws of quantum thermodynamics.

Prof. Matteo Paris
An invitation to quantum metrology

Quantum detection and estimation theory is a powerful tool
for the quantum characterization of states and operations
and for the search of new physics in different directions
at the forefront of research. In these lectures we provide
an introduction to quantum enhanced tecniques for state
discrimination and precision measurements, i.e. those schemes
often referred to as quantum metrology:

1. Generalities about estimation, measurement and discrimination;
2. Ambiguous state discrimination (Bayes and NP strategies);
3. Unambiguous state discrimination (outline);
4. Global quantum estimation theory, estimation of a shift-parameter;
5. Local quantum estimation theory, quantum Cramer-Rao theorem;
6. Examples.