Speakers

• Pasquale Calabrese, SISSA, Trieste
  
  
  
  Entanglement and thermodynamics in non-equilibrium isolated quantum systems

  Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. In the last decade the study of the non-equilibrium dynamics of isolated quantum systems revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems.
• Horacio Casini, Centro Atómico Bariloche
  
  
  
  Entanglement entropy and Lorentz symmetry in quantum field theory
  

  I will describe expected general features of entanglement entropy in quantum field theory, and how strong subadditivity is related to irreversibility theorems for the renormalization group flow for d=2,3 and 4. An important property underlying these theorems is the saturation of strong subadditivity (Markov property) for regions on the null cone. I will briefly describe other applications of entanglement entropy such as the proof of the Bekenstein bound.
• Stefan Hollands, Universität Leipzig
  
  
  
  Entanglement and modular theory
  

  The concept of entanglement and the study of entropy-like quantities describing it originated in quantum information theory. These concepts are now widely applied, including to relativistic quantum field theories. Modular theory (of v. Neumann algebras) originated in statistical mechanics and operator algebra theory, and was subsequently seen to also play an important conceptual role in relativistic quantum field theory. It turns out that ideas from this theory are very natural and useful when analyzing entanglement measures in quantum field theories. In this talk, I describe some of these connections. (Joint work with Ko Sanders.)
• Giuseppe Marmo, Università Federico II, Napoli
  
  Manifold picture of quantum mechanics, application to information geometry
  

  Pure states of any quantum system are described by a Hilbert Manifold. This manifold is a complex projective space associated with any Hilbert space, either finite or infinite dimensional. For simplicity we shall consider only finite dimensional Hilbert spaces. Once we get rid of the linear structure we have to find a replacement for linear Hermitian operators (observables) and linear unitary operators describing the evolution. We use the bidifferential operators associated with the Hermitian tensor field written in contravariant form to realize the C*-algebra of operators by means of smooth functions on the manifold. As we consider our manifold to be a real differential manifold, we naturally have a Lie-Jordan algebra. To be able to describe decoherence we consider the space of mixed states which is not smooth but a stratified manifold, at the quantum level relative entropies will play the role of classical divergence functions and allow us to construct quantum metrics with the required monotonicity properties under completely positive maps.
• Pieter Naaijkens, Universität Aachen
  
  
  
  The Jones index and channel capacities
  

  A fundamental question in quantum information theory is how much information one can send (on average) through a quantum channel. This is called the capacity of a channel. After reviewing the basics for finite dimensional systems, I will turn to wiretapping channels. Here an additional constraint is that an eavesdropper, which has limited access to the information sent via the quantum channel, cannot find out anything about the message that we want to send through the channel. I will argue that subfactor theory naturally leads to examples of such channels in infinite dimensional systems, and the Jones index is related to the capacity of the channel. Finally, I will discuss some examples form physical systems where such subfactors arise naturally.
• Mihály Weiner, Budapest University of Technology and Economics
  
  
  
  Locality and a bound on entanglement assistance to classical communication
  

  A physical theory respecting locality should not allow signaling between spacelike separated parts. However, in itself the "no-signaling" condition does not imply that cross-correlations must fit in the framework of quantum physics. Quantum correlations - unlike classical ones - can violate the Bell inequality, but e.g. they do satisfy Tsirelson's bound which in general are exceeded by non-signaling correlations.
  Many physical principles have been proposed to explain the non-existence of "super-quantum" correlations. A notable one is "Information Causality", which is expressed in terms of mutual information. However - as we did in the previous article "Classical information storage in an n-level quantum system" - instead of inequalities regarding entropy-related quantities, here we consider the question of exact classical simulations.
  Suppose Alice receives an X ∈ {0,1}ⁿ but can send only m < n classical bits (cbits) to Bob, who then needs to assign a value to Z. The "transfer matrix" (p(Z=z|X=x))_{x,z} they realize depends on their strategy and the resources they can use. In general, having a shared quantum bipartite system in some entangled state also allows them to realize transfer matrices impossible to achieve classically. However, in contrast to the generic non-signaling case, it seems (and in some cases we prove) that here the transmission of m cbits + the use of a quantum bipartite system - regardless of its size - can be always simulated by a transmission of 2m cbits. I will comment on physical interpretations and on how this could be seen as a constraint on the possible convex structure of the state-space of a system. (Work in progress; joint with P.E. Frenkel.)