Concepts and applications of quantum measurement

Thesis

In this thesis I discuss the nature of ‘measurement’ in quantum theory. ‘Measurement’ is associated with several different processes: the gradual imprinting of information about one system onto another, which is well understood; the collapse of the wavefunction, which is ill-defined and troublesome; and finally, the means by which inferences about unknown experimental parameters are made.

I present a theoretical extension to an experimental proposal from Leggett and Garg, who suggested that the quantum-or-classical reality of a macroscopic system may be probed with successive measurements arrayed in time. The extension allows for a finite level of imperfection in the protocol, and makes use of Leggett’s ‘null result’ measurement scheme. I present the results of an experiment conducted in Oxford that, up to certain loopholes, defies a non-quantum interpretation of the dynamics of phosphorous nuclei embedded in silicon.

I also present the theory of statistical parameter estimation, and discover that a recent trend to employ time symmetric ‘postselected’ measurements offers no true advantage over standard methods. The technique, known as weak-value amplification, combines a weak transfer of quantum information from system to meter with conditional data rejection, to surprising effect. The Fisher information is a powerful tool for evaluating the performance of any parameter estimation model, and it reveals the technique to be worse than ordinary, preselected only measurements. That this is true despite the presence of noise (including magnetic field fluctuations causing deco- herence, poor resolution detection, and random displacements), casts serious doubt on the utility of the method.

Authors: Knee, G

• Publication date: 2014
• DOI: 10.5287/ora-9gmy0vorq
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: Weak value; weak measurement; null result measurement; parameter estimation; quantum measurement; Fisher information; venality; amplification; measurement; Leggett-Garg; Macrorealism; Quantum theory
• Subjects: Quantum information processing; Philosophy of physics; Quantum theory (mathematics); Atomic and laser physics; Theoretical physics; Condensed matter theory