These lectures will provide advanced theoretical tools to understand and model quantum open systems (quantum systems coupled to a dissipative environment), with constant opening on foundational questions of quantum mechanics, e.g. the famous “measurement problem”. The last series of lectures will focus on the entropic and energetic aspects of quantum information.

Chapter 1: Quantum measurement

- Reminders on quantum entanglement, the Von Neumann model for quantum measurement, Schrödinger cat states, decoherence.

- Which path experiments, complementarity, weak and strong measurements, quantum non- demolition measurements, POVM (positive-operator valued measure).

- Interpretations of quantum theory: where are we?

- Beyond Heisenberg limit: elements of quantum metrology.

Chapter 2: Quantum open systems:

- Quantum processes: Completely Positive Trace Preserving Maps, Kraus operators, Chi matrix.

- Dynamic of open quantum systems: Lindblad equation, physical examples of quantum noises and decoherence processes.

- Quantum trajectories measurements (photo-counting, homodyne vs heterodyne measurements).

- Modeling noise: input-output theory, repeated interactions approaches.

Chapter 3: Advanced quantum information

- Measuring (quantum) information and entanglement: Shannon entropy, von Neumann entropy and their operational meaning (data compression theorems). Entropy of entanglement, entanglement witnesses.

- Quantum information thermodynamics: logical/thermodynamical irreversibility, Maxwell’s demon, Landauer’s erasure bound, work value of entanglement and coherence, energetic advantage of quantum computing.

Prerequisites:

Quantum Mechanics M1

Statistical physics M1

References:

Exploring the quantum (Haroche & Raimond, Cambridge University Press)

Quantum measurement and control (Wiseman & Milburn, Cambridge University Press)

Quantum computation (Online lectures by John Preskill)