Advanced Quantum Information course

Quantum Information Theory forms the underpinning for many modern devices that exploit quantum effects. The focus of this course lies on providing an introduction to the principles of this theory, as well as a presentation of some of its more specialized aspects. The course begins by describing the kinematic and dynamical building blocks of quantum information theory. After introducing the notion of entanglement and correlations in quantum states, it will offer an overview over existing distance and entropy measures in quantum mechanics, followed by an exploration of the concept of recoverability of quantum information via so-called Petz maps. Placing some emphasis on numerical methods, the course will then touch upon semidefinite programming as a versatile tool for quantum optimization problems, and end with a presentation of higher order quantum maps and their usage in the field of open multi-time quantum stochastic processes.

Details and materials

As a prerequisite, the course assumes basic familiarity with quantum mechanics and linear algebra, but is otherwise self-contained.

Students who successfully complete the course will have gained familiarity with:

  • quantum states and density matrices, quantum channels and quantum measurements
  • distances in quantum state space and quantum entropies
  • measurement disturbance and quantum discord
  • recoverability of quantum evolution
  • methods of semidefinite programming in quantum science
  • higher order quantum architectures and multi-time quantum stochastic processes

Dr. Simon Milz (milzs@tcd.ie) and Prof. Felix Binder (felix.binder@tcd.ie)

Fitzgerald Library, Fitzgerald Building

Wednesdays 5-7pm, starting 31 January

Note. The doors of the Fitzgerald Building may be closed at the time of the lecture. If so, we suggest going through the SNIAM building instead.

The programme of the lectures is subject to change. The digital chalkboard for the lectures will be uploaded in this section as soon as it is made available.

L1 31.01 Felix Binder Introduction and recap. Quantum states, states space, operators, composite systems

L2 L2s

7.02 Felix Binder More on quantum states (the notes marked as L2s refer to the supplement given the following week)
L3 14.02 Simon Milz Dynamics: quantum channels and measurements
L4 21.02 Simon Milz Channel representations
L5 28.02 Felix Binder Entanglement and quantum resource theories
--     Study Week
L6 13.03 Alessandro Candeloro Measurement disturbance, classical-quantum states, Holevo information and quantum disturb
L7 20.03 Alec Boyd Recovery maps
L8 27.03 Simon Milz Semidefinite programming
L9 3.04 Simon Milz Higher-order quantum maps
L10 10.04 Simon Milz Quantum stochastic processes and the process tensor formalism