141.282 Quantum Information Theory I
This course is in all assigned curricula part of the STEOP.
This course is in at least 1 assigned curriculum part of the STEOP.

2023W, VO, 2.0h, 3.0EC


  • Semester hours: 2.0
  • Credits: 3.0
  • Type: VO Lecture
  • Format: Presence

Learning outcomes

After successful completion of the course, students are able to understand and apply the fundamental concepts in quantum information science. Specifically, the students will acquire the necessary theoretical skills for

(1) formally describing quantum information systems,

(2) identifying, characterizing, and quantifying entanglement,

(3) understanding paradigmatic protocols for quantum communication

Subject of course

   Basic formalism of quantum information

1.1    Pure and Mixed Quantum States: Hilbert space, pure states, review of Dirac notation, qubits, linear operators, Hermitian operators, unitary operators, projectors, expectation values, trace, mixedness/linear entropy, time evolution, Bloch decomposition, single-qubit examples.
1.2    Composite Systems: Tensor products of vectors and operators, expectation values, partial trace, reduced states, generalized Bloch decomposition
1.3    Entropy of Quantum States: Shannon & von Neumann entropy, properties, entropy of bipartite systems, subadditivity, Araki-Lieb inequality, concavity, relative entropy
1.4    Schmidt Decomposition & Purification: Schmidt decomposition theorem and proof, purification of mixed quantum states
1.5    Hilbert Space Geometry: Overlap of quantum states, Uhlmann fidelity, Uhlmann theorem, Bures distance, trace distance, relative entropy revisited

2    Entanglement & Correlations

2.1     Entanglement of Pure and Mixed States: Separability of pure states, entropy of entanglement, Example: Bell states, separability of mixed states, classical correlations vs. entanglement, mutual information
2.2    Entanglement and Nonlocality: EPR Paradox, Bell inequalities, CHSH inequalities, entanglement vs. non-locality, Tsirelson´s bound
2.3    Separability Criteria: Peres-Horodecki criterion, realignment criterion, Example: Werner states, CHSH criterion
2.4    Geometry of Entanglement: Convex structure of state space, entanglement witnesses. Example: geometry of Bell-diagonal states
2.5    Entanglement Quantification: LOCC, Nielsen majorization, entanglement monotones vs. entanglement measures, negativity, entanglement of formation, concurrence, monogamy of entanglement

Teaching methods

Lecture with active students' participation.

Mode of examination




Course dates

Thu14:00 - 16:0005.10.2023 - 25.01.2024Seminarraum ZE 01 - 1 Lecture
Quantum Information Theory I - Single appointments
Thu05.10.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu12.10.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu19.10.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu09.11.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu16.11.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu23.11.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu30.11.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu07.12.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu14.12.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu21.12.202314:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu11.01.202414:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu18.01.202414:00 - 16:00Seminarraum ZE 01 - 1 Lecture
Thu25.01.202414:00 - 16:00Seminarraum ZE 01 - 1 Lecture

Examination modalities

Oral exam at the end of the lecture

Course registration

Not necessary


Study CodeObligationSemesterPrecon.Info
066 461 Technical Physics Mandatory elective
066 461 Technical Physics Mandatory elective


No lecture notes are available.

Previous knowledge

Linear algebra,

knowledge of quantum mechanics is helpful (and recommended) but not strictly necessary