Suguru Furuta
Control and Measurement of Quantum Spins: Theory and Simulations
PhD Thesis (2005)

The theory of quantum computation has established the striking fact that a quantum computer processor can unlock extraordinary computational power from simply the light and matter that make up the universe. This discovery created a surge of renewed interest in the technological applications of low-dimensional quantum systems, such as the polarization of the photon or the spin of the electron. In quantum information processing tasks, these play important roles as natural repositories for irreducible units of quantum information: qubits. This thesis examines the control and measurement of quantum spins from both technological and fundamental viewpoints. The control and measurement of low-dimensional quantum systems are important requirements for the practical implementation of quantum information processing tasks. They are also of fundamental importance because of the still controversial issue of how we are to interpret quantum theory. In particular, the quantum measurement of spin offers many opportunities for interesting discussions on this issue. This thesis features the following four main topics of interest: the Stern-Gerlach measurement, spintronics and quantum computation, the characterization of spin decoherence processes, and the extension of the causal interpretation of quantum theory to Dirac theories of many spin-1/2 particles. The field of quantum information science is a strongly inter-disciplinary field, and this is reflected in the multi-faceted nature of this thesis. We first compare and contrast the classical and the quantum descriptions of the Stern-Gerlach experiment to highlight its historical significance. We discuss the Bohr-Pauli assertion, which states that it is impossible to perform a Stern-Gerlach measurement of the electron spin by means of experiments based on the concept of classical particle trajectories. We refute the generalized quantum form of this assertion. Next, we turn to quantum computation with electron spins in quantum dots. Focusing on one implementation scheme in particular, we rigourously model the dynamics of electron spins trapped in surface acoustic waves. We confirm that single-qubit operations can indeed be accomplished using nanomagnets, but we also show that Lorentz force effects do matter. This work clarifies this issue, which has hitherto gone largely unnoticed. Still on the subject of quantum control, we review the theory of open spin systems and apply it to an N-spin toy decoherence model whose behaviour for large N demonstrates the emergence of classicality. We then develop a novel method based on perturbation theory, which enables one to characterize incoherent quantum noise from experimental data and subsequently to counteract it. Lastly, we turn to the causal interpretation of quantum theory. We first argue the importance of using multiparticle trajectories to account for decoherence, rather than the reduced single-particle trajectories used in other studies. Furthermore, we compare and contrast different approaches to a multiparticle causal Dirac theory. Our Lorentz invariant approach meets one key interpretational problem concerning the equivariance and statistical transparency of the probability distribution. This raises important questions as to the validity of the Bohmian approach to quantum theory.

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