Open Quantum Systems, Mathematical and Thermodynamical Aspects

Scientific training, by Alexia Auffèves and Alain Joye
Open quantum systems, at the basis of out-of-equilibrium statistical mechanics and quantum thermodynamics, also play a key role in quantum engineering where the control of the decoherence and entanglement of quantum bits is of paramount importance. This course presents the concepts and mathematical tools necessary to describe and analyze some of their dynamical properties, as well as a view to the recent experimental and theoretical developments in the fast-growing field of quantum thermodynamics.
This program is well suited to the Grenoble site, which has international visibility in the field, both from the point of view of theoretical (LPMMC, Néel, Institut Fourier) and experimental research (experiments in optomechanics, mesoscopic physics, quantum electrodynamics circuits...), and is home to many doctoral students and young researchers to which it should be profitable.

Course Structure

18 hours course, which would be given in 6 times 3 hours. Here are the provisional headings:

Quantum systems in (infinite) dimension: quantum states, density and observable matrices, pure / mixed states, Gibbs states, and entropy. Bi-partite systems, Schmidt decomposition, separable and entangled states, partial trace, relative entropy.

Open Systems and Quantum Operations: Completely Positive Applications, Quantum Channels and their Adjoints, Stinespring and Kraus Representations, Spectral Properties. Effective evolution and quantum measurements. Landauer’s Principle.

Quantum dynamical system: invariant states, Liouvillian, ergodicity properties, KMS states. Weak limit, Markov approximation, quantum semi-group, Lindbladian. Repeated quantum interactions, large times Asymptotics.

Entropy production, evolution of entanglement, decoherence. Protocols of two-step measurements, quantum trajectories, complete statistics and large deviations. Time reversal, Gallavotti-Cohen symmetry.

Basics of information thermodynamics, reversible energy-information conversion (Landauer initialization, Szilard machine, Maxwell's demon), experimental achievements. Impact on the energetics of classical computing.

Generalized fluctuation theorems (with information extraction and feedback), absolute irreversibility.

Quantum work and heat, quantum machines, energy counterpart of coherence and quantum measurement. Impact on the energetics of quantum computing.

Timetable :

Session n° 1
Date : 12-04-2018
Time : 9h - 12h00
Session n° 4
Date : 03-05-2018
Time : 9h - 12h00
Session n° 2
Date : 19-04-2018
Time : 9h - 12h00
Session n° 5
Date : 17-05-2018
Time : 9h - 12h00
Session n° 3
Date : 27-04-2018
Room K223
Time : 9h - 12h00
Session n° 6
Date : 01-06-2018
Room E424
Time : 9h - 12h00

Published on May 22, 2018