Error Models for Quantum State and Parameter Estimation

Abstract

Within the field of Quantum Information Processing, we study two subjects: For quantum state tomography, one common assumption is that the experimentalist possesses a stationary source of identical states. We challenge this assumption and propose a method to detect and characterize the drift of nonstationary quantum sources. We distinguish diffusive and systematic drifts and examine how quickly one can determine that a source is drifting. Finally, we give an implementation of this proposed measurement for single photons.

For quantum computing, fault-tolerant protocols assume that errors are of certain types. But how do we detect errors of the wrong type? The problem is that for large quantum states, a full state description is impossible to analyze, and so one cannot detect all types of errors. We show through a quantum state estimation example (on up to 25 qubits) how to attack this problem using model selection. We use, in particular, the Akaike Information Criterion. Our example indicates that the number of measurements that one has to perform before noticing errors of the wrong type scales polynomially both with the number of qubits and with the error size.

This dissertation includes previously published co-authored material.