## Quantum Information: Anna Sanpera

Quantum information in strongly correlated systems

Quantum Information is having a profound impact in several areas of physics ranging from quantum optics, quantum many-body systems, or high energy physics just to mention some. In this lectures we will focus in strongly correlated systems and in the plethora of exciting phenomena that such systems present. We will then approach these systems from a quantum information perspective analyzing the behaviour displayed by the quantum correlations present in the system. We will see that this approach allows us to recover well stablished condensed matter concepts such as criticality, universality and quantum phase transitions and to link symmetries and conformal field theory to quantum information quantities. In the second lecture we will discuss bipartite versus multipartite entanglement in strongly correlated systems and briefly overview many most open questions in the subject.

Quantum Information is having a profound impact in several areas of physics ranging from quantum optics, quantum many-body systems, or high energy physics just to mention some. In this lectures we will focus in strongly correlated systems and in the plethora of exciting phenomena that such systems present. We will then approach these systems from a quantum information perspective analyzing the behaviour displayed by the quantum correlations present in the system. We will see that this approach allows us to recover well stablished condensed matter concepts such as criticality, universality and quantum phase transitions and to link symmetries and conformal field theory to quantum information quantities. In the second lecture we will discuss bipartite versus multipartite entanglement in strongly correlated systems and briefly overview many most open questions in the subject.

## Quantum thermodynamics: Vlatko Vedral

Three roads to quantum thermodynamics

The laws of thermodynamics need to be generalized to the finite, quantum, non-equilibrium domain. It is by no means clear how to achieve this. In particular, how exactly are we to phrase the concepts of heat, work and entropy in the most general context?

I plan to review three of the most relevant approaches. The first is based on what is called the “resource theory”, the second is known as the “single shot thermodynamics” and the last is based on the non-equilibrium fluctuation-dissipation (Jarzynski) relations. I will first review each of the approaches and then, based on this, I will argue that: a) the usual entropies (due to Shannon and von Neumann, classically and quantumly respectively) are not sufficient to discuss state transformations (we need a more general concept of “majorisation”); b) the relationship between information and work requires us to use more generalized (Renyi) entropies; c) work is, in the quantum setting, not represented by an operator; d) any conclusions are highly sensitive to how we define the “rules of the game”; e) we need to include finite time transformations.

These are just some of the issues we need to face, but there may be others en route to formulating the most general theory of thermodynamics. This is, of course, not only of pure academic interest, but is becoming of practical importance though our advances in the nano- and quantum technologies. I will also draw parallels between how we understand entanglement through local operation and how we formulate thermodynamical entropy.

The laws of thermodynamics need to be generalized to the finite, quantum, non-equilibrium domain. It is by no means clear how to achieve this. In particular, how exactly are we to phrase the concepts of heat, work and entropy in the most general context?

I plan to review three of the most relevant approaches. The first is based on what is called the “resource theory”, the second is known as the “single shot thermodynamics” and the last is based on the non-equilibrium fluctuation-dissipation (Jarzynski) relations. I will first review each of the approaches and then, based on this, I will argue that: a) the usual entropies (due to Shannon and von Neumann, classically and quantumly respectively) are not sufficient to discuss state transformations (we need a more general concept of “majorisation”); b) the relationship between information and work requires us to use more generalized (Renyi) entropies; c) work is, in the quantum setting, not represented by an operator; d) any conclusions are highly sensitive to how we define the “rules of the game”; e) we need to include finite time transformations.

These are just some of the issues we need to face, but there may be others en route to formulating the most general theory of thermodynamics. This is, of course, not only of pure academic interest, but is becoming of practical importance though our advances in the nano- and quantum technologies. I will also draw parallels between how we understand entanglement through local operation and how we formulate thermodynamical entropy.

## Foundations of quantum mechanics: Roger Colbeck

Are there random processes in nature?

Quantum mechanics is one of the most successful physical theories. One of the central ways in which it differs from classical theory is that it does not in general give deterministic predictions. In my lectures, I will discuss the evidence we have for random processes in nature, and how we might verify their presence in a theory-independent way (i.e., without relying on quantum mechanics). In doing so, we will cover the EPR paradox and Bell's theorem before pushing towards some recent results that give arguably the strongest evidence for randomness to date.

Quantum mechanics is one of the most successful physical theories. One of the central ways in which it differs from classical theory is that it does not in general give deterministic predictions. In my lectures, I will discuss the evidence we have for random processes in nature, and how we might verify their presence in a theory-independent way (i.e., without relying on quantum mechanics). In doing so, we will cover the EPR paradox and Bell's theorem before pushing towards some recent results that give arguably the strongest evidence for randomness to date.