"Quantum Paradoxes: Quantum Theory for the Perplexed"
Yakir Aharonov, Daniel Rohrlich
WILEY-VCH, 2005
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"Quantum theory of phase estimation", L' Pezzè and A. Smerzi,
https://arxiv.org/abs/1411.5164
Learning Objectives
The course will illustrate fundamental and foundational aspects of quantum mechanics with applications on quantum interferometry
Prerequisites
It is highly advisable that the student has a good knowledge and understanding
of quantum mechanics
Teaching Methods
lectures provided on the blackboard
Type of Assessment
oral exam
Course program
I) Paradoxes.
• On the many interpretations of the Heisenberg uncertainty relations
• The Einstein-Podolski-Rosen paradox and the concept of entanglement
• Bell inequality: the violation of local realism
• The double slit and the “quantum eraser’’ experiments
• The problem of measurement in quantum mechanics.
i) Copenhagen interpretation; ii) Bohmian quantum mechanics;
iii) Many worlds interpretation
• Weak, quantum non demolition & interaction-free measurements
• Superluminal signalling and “no-go theorems”
• Geometrical phases (Berry’s and Aharonov-Anandan phases)
• Zeno paradox in quantum mechanics
• Time in quantum mechanics
II) Quantum Interferometry
• What is "probability" ? Bayesian versus frequentist
• Phase estimation: “maximuum likelihood” and Bayesian confidence
• Spin-squeezing
• Fisher information
• Useful entanglement
• From shot-noise to Heisenberg limit in precision measurements