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Quantum effects [MA5047]

Wintersemester 2013/14

Prof. Dr. Michael M. Wolf

Dozent: Prof. Dr. Michael M. Wolf
Übungsleitung: Martin Idel
Mitwirkende:  
Vorlesung: Mo 13:55-15:25, Raum 03.10.011 Anmeldung
Zentralübung: Di 14:00-16:00, Raum 03.08.011 Anmeldung
Tutorübungen:   Anmeldung

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Content

The lecture will first introduce the mathematical framework of quantum theory, from an abstract (mostly information theoretic) perspective focussing on completely positive maps. On this basis we will then visit many quantum effects and phenomena such as uncertainty relations, no-cloning, teleportation, entanglement and the non-existence of local hidden variable theories, etc. The aim of the lecture is to provide a quick introduction to modern quantum theory from an abstract operational point of view - quite orthogonal to many traditional quantum theory lectures.

Lecture Notes

Handwritten notes:
File Version Topics Comments
lecture 1 14.10.2013 Historical remarks, Hilbert spaces, Bounded operators  
lecture 2 28.10.2013 Density operators, POVMs, probabilities incl. examples discussed in lec.3
lecture 3 28.10.2013 Observable, uncertainty relations, joint measurability  
lecture 4 19.11.2013 Composite systems, tensor products, Schmidt decomposition, partial trace  
lecture 5 19.11.2013 Purification, entanglement, local hidden variable theories  
lecture 6 25.11.2013 LHV theories, Bell inequalities, CHSH, Bell violation, Cirelson bound  
lecture 7 3.12.2013 Bell ineq.s and Grothendiek's constant, chain of impossible machines  
lectures 8/9 30.12.2013 complete positivity, quantum channels, Stinespring dilation, no-signalling, no-cloning  
lecture 10 12.01.2014 instruments, no-information-without-disturbance, entanglement assisted teleportation  
lectures 11/12 27.01.2014 Monogamy, frustration, quantum De Finetti theorem  

Preliminary latex version of lecture 1-10.

Exercises

File due date Topics Solutions
sheet 1 29.10.2013 trace norm, commutators, Bloch sphere solution 1
sheet 2 12.11.2013 commutators, uncertainty relations, tensor products solution 2
sheet 3 26.11.2013 tensor products, reduced density matrices solution 3
sheet 4 10.12.2013 Bell inequalities, LHV models solution 4
sheet 5 14.01.2013 quantum channels solution 5
sheet 6 21.01.2013 teleportation, commutant, dense coding solution 6
sheet 7 04.02.2013 monogamy, instruments, unitary freedom, separability (added a few details in the proof of ex. 4) solution 7

Literature