Quantum Measurement and Estimation Theory

fizyka

Familiarity with quantum mechanics and linear algebra. Previous contact with quantum information and quantum optics is welcomed, though not indispensable.

w sali

1. Quantum measurements

- quantum measurement mathematical formalism

- decoherence mechanisms

- weak and strong measurements

- joint measurements of non-commuting observables

2. Classical estimation theory

- Fisher information, Cramer-Rao bound

- Maximum likelihood estimation

- Bayesian estimation

3. Quantum estimation theory

- discrimination of quantum states

- quantum Fisher information

- optimal Bayesian quantum estimation

- covariant measurements

4. Quantum metrology

- Quantum channel estimation

- Optimal phase estimation

- Practical quantum enhanced metrological schemes (squeezed states of light, spin-squeezed states)

- Impact of decoherence on quantum enhanced protocols

- Fundamental bounds in quantum metrology

- Practical applications: gravitational wave detectors, atomic clocks

S. M. Kay "Fundamentals of statistical signal processing: estimation theory"

C. W. Helstrom "Quantum detection and estimation theory",

A. S. Holevo "Probabilistic and Statistical Aspects of Quantum Theory"

Understanding of limitations imposed by quantum mechanics on measurement precision. Ability to formulate optimization problems to find optimal measurement strategies. Applications of the knowledge of non-classical states of light and atoms in proposing interferometric schemes with quantum enhanced precision (with potential use in devices such as gravitational wave detectors or atomic clocks).

Homework problems, Exam