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Quanteninformation
Quantum Information

Modul PH2237

Diese Modulbeschreibung enthält neben den eigentlichen Beschreibungen der Inhalte, Lernergebnisse, Lehr- und Lernmethoden und Prüfungsformen auch Verweise auf die aktuellen Lehrveranstaltungen und Termine für die Modulprüfung in den jeweiligen Abschnitten.

Modulversion vom WS 2017/8

Von dieser Modulbeschreibung gibt es historische Versionen. Eine Modulbeschreibung ist immer so lange gültig, bis sie von einer neuen abgelöst wird.

verfügbare Modulversionen
WS 2018/9WS 2017/8WS 2016/7

Basisdaten

PH2237 ist ein Semestermodul in Englisch auf Master-Niveau das im Wintersemester angeboten wird.

Das Modul ist Bestandteil der folgenden Kataloge in den Studienangeboten der Physik.

  • Allgemeiner Spezialfachkatalog Physik
  • Spezifischer Spezialfachkatalog Physik der kondensierten Materie
  • Spezialisierung im Elitemasterstudiengang Theoretische und Mathematische Physik (TMP)

Soweit nicht beim Export in einen fachfremden Studiengang ein anderer studentischer Arbeitsaufwand ("Workload") festgelegt wurde, ist der Umfang der folgenden Tabelle zu entnehmen.

GesamtaufwandPräsenzveranstaltungenUmfang (ECTS)
150 h 45 h 5 CP

Inhaltlich verantwortlich für das Modul PH2237 in der Version von WS 2017/8 war Norbert Schuch.

Inhalte, Lernergebnisse und Voraussetzungen

Inhalt

Quantum Information deals with the study of quantum mechanics from the point of view of information theory, as well as with the use of quantum mechanical systems for the purpose of information processing and computation. On the one hand, this includes quantum information theory, with topics such as quantum teleportation, the transmission of information through quantum channels, quantum cryptography, and the quantification of quantum entanglement as a resource for the aforementioned tasks. On the other hand, it involves quantum computation, i.e., computation based on the laws of quantum mechanics, covering topics such as quantum algorithms, quantum error correction, and the physical realization of quantum computers.

The lecture provides a comprehensive introduction to the field of Quantum Information.  It covers:

  • States, evolution, and measurement
  • Quantum entanglement
  • Quantum channels
  • Quantum cryptography
  • Quantum computation and quantum algorithms
  • Quantum error correction
  • Implementations of quantum information processing

Lernergebnisse

After successful completion of the module the students:

  1. are able to explain the pure and mixed state formalism of quantum mechanics
  2. understand the Bloch sphere picture
  3. are familiar with the Schmidt decomposition, its relevance for understanding entanglement, and purifications of mixed states
  4. can explain completely positive maps and their relevance, the Kraus representation, and the Stinespring dilation
  5. know about POVM measurements and their relation to projective measurements
  6. understand pure state entanglement, in particular the relevance of the entropy of entanglement
  7. know about basics of mixed state entanglement, in particular the PPT criterion, entanglement witnesses, and negativity
  8. understand the importance of Bell inequalities
  9. have learned the basics of quantum computing, in particular quantum circuits, the role of reversibility, and basic alsorithms, in particular the Deutsch algorithm, Grover's algorithm, and Shor's algorithm
  10. know basics of quantum error correction, in particular the 9-qubit Shor code

Voraussetzungen

Very good knowledge of Linear Algebra is essential for this lecture. Knowledge of quantum mechanics is certainly useful, but not strictly necessary. (However, please let the lecturer know in advance should you have no prior knowledge of quantum mechanics.)

Lehrveranstaltungen, Lern- und Lehrmethoden und Literaturhinweise

Lehrveranstaltungen und Termine

ArtSWSTitelDozent(en)Termine
VO 2 Quantum Information Schuch, N. Fr, 14:00–16:00, PH HS2
UE 1 Exercise to Quantum Information Schuch, N. Termine in Gruppen

Lern- und Lehrmethoden

The lecture will be taught on the blackboard.  Lecture notes will be published on the lecture website http://www.mpq.mpg.de/~nys/QI1718.  The lecture will be complemented by homework sheets and tutorials, which serve to deepen the understanding of the topics covered in the lecture through specific examples and complementary perspectives.  Study of the homework sheets and attendance of the tutorials is therefore strongly encouraged.

Medienformen

blackboard presentation, lecture notes, homework sheets

Literatur

  • J. Preskill, Quantum Computation lecture notes.
  • M. Nielsen and I. Chuang, Quantum Information and Computation. (Cambridge University Press, 2010)

Additional literature may be given during the lectures.

Modulprüfung

Beschreibung der Prüfungs- und Studienleistungen

There will be an oral exam of about 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and examples.

For example an assignment in the exam might be:

  • How does the Deutsch algorithm work?
  • What is a completely positive map?
  • What is the Bloch sphere?
  • What is the idea behind quantum error correction?
  • What is the PPT criterion?
  • What is the Schmidt decomposition, and what is its relevance to entangement?
  • What is a purification of a mixed state?
  • What happens to continuous erros in quantum error correction?
  • How can we find a Schmidt decomposition?
  • What is the Choi-Jamiolkowski isomorphism?

Participation in the tutorials is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

Wiederholbarkeit

Eine Wiederholungsmöglichkeit wird am Semesterende angeboten.

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