Quantum local asymptotic normality and other questions of quantum statistics

Kahn, J. (2008)

Doctoral Thesis

This thesis is entitled Quantum Local Asymptotic Normality and other questions of Quantum Statistics ,. Quantum statistics are statistics on quantum objects. In classical statistics, we usually start from the data. Indeed, if we want to predict the weather, and can measure the wind or the temperature, we can measure both. On the other hand the laws of physics themselves forbid us to measure simultaneously the speed and the position of an electron. We therefore have to start with the observed object itself, and choose the best measurement for our purposes. My main result is that, for all statistical purposes, numerous copies of the same spin (magnetic state of an electron) is equivalent to a Gaussian state of a quantum harmonic oscillator, typically laser light. We can extend this to higher dimensions. As an application, we get an (asymptotically) optimal estimation scheme for unknown spins. The idea is to transform the spins into laser light, and use the already known optimal estimation methods for laser light. The thesis furthermore includes four smaller problems, notably how to estimate a unitary (natural) evolution very quickly, and how best to decide which is the state of a quantum object, among a finite number

• Discrimination
• Estimation
• Group representations
• Local asymptotic normality
• Minimax
• POVM
• Quantum stochastic differential equations
• Special unitary

• All authors: Kahn, J.
• Supervisor: Gill, R.
• Co-supervisor: Massart, P.
• Qualification: Doctor (dr.)
• Awarding Institution: Faculty of Science, Leiden University
• Date: 2008-06-17
• ISBN (print): 9789090232546