## Quantum effects [MA5047]

### Wintersemester 2013/14

### Prof. Dr. Michael M. Wolf

Dozent: |
Prof. Dr. Michael M. Wolf | |

Übungsleitung: |
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Mitwirkende: |
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Vorlesung: |
Mo 13:55-15:25, Raum 03.10.011 | Anmeldung |

Zentralübung: |
Di 14:00-16:00, Raum 03.08.011 | Anmeldung |

Tutorübungen: |
Anmeldung |

### News

- Re-examination will be on April 2nd, 11:00 in room 00.07.014.
- Examination will be on Feb. 28th., 10:30-11:30, MI HS3 (00.06.011). It will be a written test; auxiliary material/media won't be allowed.
- Lecture notes now available as latex/pdf (lecture 1-10)
- The lecture starts at 13:55 sharp

### 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 |

### 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

- for the mathematical background (lectures 1,2,4): e.g. chapter 2 in Alicki, Fannes: "Quantum dynamical systems", Oxford University Press, or chapters 1,2 in Alexander Holevo: "Statistical Structure of Quantum Theory", Springer. The latter also covers most of lecture 3.