**Collection Number**C17037

**Collection Date**-

**Collection Type**Course

## PSI 2017/2018 - Quantum Theory - Lecture 14

Bell/CHSH theorem and non-locality: proof; Contextuality (Peres-Mermin proof).

## PSI 2017/2018 - Quantum Theory - Lecture 13

Entanglement and non-locality - Criteria for mixed-state entanglement - Physical significance of entanglement (CHSH game) - Bell experiment/CHSH inequality

## PSI 2017/2018 - Quantum Theory - Lecture 12

Counter example to generalized postulate 3 and theory of entanglement; State-update rule under POVM - Entanglement and non-locality - Entropy.

## PSI 2017/2018 - Quantum Theory - Lecture 11

Generalized transformationsv - Kraus decomposition - Example: CNOT gate - Stinespring dilation theorem - Postulate 3 - Counter example.

## PSI 2017/2018 - Quantum Theory - Lecture 10

Generalized Measurement: Mathematical structure - POVM - Postulate 2 (Discrete case) - POVM Continuous case - Postulate 2 (Continuous case) - Example: Trine POVM measurement - Naimark/Neumark's dilation theorem - Generalized transformations: Postulate 3.

## PSI 2017/2018 - Quantum Theory - Lecture 9

Theory of Quantum Measurement - Von Neuman inderect measurement model - Inconsistency btw result obtained from Schrödinger eq and from State update rule - Stern-Gerlach example.

## PSI 2017/2018 - Quantum Theory - Lecture 8

Real-world quantum systems description - Pure state vs Mixed states - Purification of Mixed States; Generalized measurement - Mixtures of "ideal measurement" - Ideal measurement of a composite system - POVMs.

## PSI 2017/2018 - Quantum Theory - Lecture 7

Infinite Dimensional Systems - Dirac's approach vs von Neumann's approach; Operational Postulates for open (real-world) quantum systems: probabilistic mixtures of pure states vs Partial description of composite system (partial trace, reduced state) - Operational postulate 1.

## PSI 2017/2018 - Quantum Theory - Lecture 6

Composite Quantum Systems - Examples and basic mathematical properties; Entanglement - Schmidt decomposition/Schmidt number; Infinite dimensional Hilbert space and unbounded operators - Dirac's approach vs von Neumann's approach.

## PSI 2017/2018 - Quantum Theory - Lecture 5

Meaning of labels; state up-date rule as a consequence of postulates; state up-date rule classically - Kochen-Specker model of qubit. Some additional references on the Kochen Specker model: Part II; Chap. D part 3.