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Roland Doll
Decoherence of spatially separated quantum bits
Supervisor: PD Dr. Sigmund Kohler [Theoretical physics I]
Date of oral examination: 02/22/2008
126 pages, english , OPUS (Online-Publikations-Server) der Universitätsbibliothek Augsburg
This work investigates the decoherence of a qubit register caused by spatially correlated quantum noise and develops theoretical tools to describe the associated reduced qubit dynamics. The environment that causes decoherence of the qubit states is modeled as a bosonic field. The non-local qubit-field coupling explicitly takes effects from a finite propagation time of field distortions between separated qubits into account. A natural realization of this model is the coupling of quantum dot spin and charge qubits to phonons of the underlying substrate. One part of the work concentrates on the case where the bath fluctuations induce pure dephasing of the qubit states. For this problem the reduced qubit dynamics possesses an exact solution which is presented in explicit form. A main focus is put on (i) the short-time dynamics of a single qubit which in the standard description with exponential decay rates shows up as a reduced initial amplitude of coherent qubit oscillations, and (ii) the consequences of a spatial qubit separation of several qubits for bipartite qubit entanglement and the register fidelity. In a second part it is shown that a direct application of the Bloch-Redfield theory to a spatially extended system of qubits leads to a violation of causality and predicts spurious decoherence-free subspaces. We reveal why this approach fails and derive a non-Markovian causal master equation that captures the main effects of the spatial separation. Compared to general non-Markovian master equations, the causal master equation has the advantage of being more intuitive and of allowing for algebraic methods, e.g. within a symmetry analysis. Finally, using the causal master equation approach the decoherence of two spatially separated qubits subject to bit-flip noise is studied. We investigate how spatial noise correlations influence the relaxation of entangled solid-state qubits. It is shown that by collective exchange of bosons via a thermal one-dimensional environment effects similar to superradiance and subradiance are possible even for rather large qubit distances and at high temperatures.