F7136 Nonlocality, Entanglement and Geometry of Quantum Systems

Faculty of Science
Autumn 2012
Extent and Intensity
2/1. 2 credit(s) (plus 2 credits for an exam). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium).
Teacher(s)
Priv.-Doz. Dr. Beatrix C. Hiesmayr (lecturer)
Priv.-Doz. Dr. Beatrix C. Hiesmayr (seminar tutor)
Guaranteed by
prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Priv.-Doz. Dr. Beatrix C. Hiesmayr
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of the course students should have a basic knowledge of how to describe single, bipartite and multipartite quantum systems, about the new potentials entangled states provide over classical ones and have gained insight into the some possible applications such as quantum cryptography.
Syllabus
  • I Density Matrix (Density Operator)
  • Description of a quantum state
  • Properties of Density Matrices
  • Equation of Motion
  • Density matrix for spin-1/2 particles, Bloch’s sphere
  • Density matrix for a pure spin state along an arbitrary direction
  • Density matrix for mixed states
  • Density matrix in thermal equilibrium
  • Composite quantum systems
  • Purification of a quantum state
  • Examples of composite states
  • II Entanglement
  • Bipartite entanglement
  • Measures of entanglement: EOF, Concurrence
  • Multipartite entanglement (basics)
  • Relativistic entanglement
  • III Quantum Teleportation
  • IV Bell Inequalities
  • The CHSH inequality
  • The Collins-Gisin-Linden-Massar-Popescu-Bell inequality
  • How to construct Bell inequalities generally
  • Examples: Photons, Neutrons
  • Examples: Kaonic Qubits
  • V Geometry of Entangled States in the Hilbert-Schmidt Space and Witnesses
  • Simplex: bipartite Qubits
  • Simplex: bipartite Qudits, bound entanglement
  • Simplex: multipartite Qubits
  • Master Equations
  • VI Quantum Cryptography and Secret Sharing
  • BB84
  • Ekert Protocol
  • Secret Sharing
Teaching methods
lectures combined with short problems that repeat, deepen and complement the subject teached; partly, there will be given time during the lectures to solve problems (in groups) and to discuss them immediately, partly, problems have to be solved at home and then presented; therefore, there will be no distinction between lecture course and problem solving course. The course will be as interactive as possible, e.g. there will be given possibilities for discussions
Assessment methods
There will be oral examinations. The problem solving part is examined by presence and presentations.
Language of instruction
English
Further Comments
The course can also be completed outside the examination period.
The course is taught only once.
The course is taught: every week.
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