Topics in Estimation of Quantum Channels

Abstract

A quantum channel is a mapping which sends density matrices to density matrices. The estimation of quantum channels is of great importance to the field of quantum information. In this thesis two topics related to estimation of quantum channels are investigated. The first of these is the upper bound of Sarovar and Milburn (2006) on the Fisher information obtainable by measuring the output of a channel. Two questions raised by Sarovar and Milburn about their bound are answered. A Riemannian metric on the space of quantum states is introduced, related to the construction of the Sarovar and Milburn bound. Its properties are characterized. The second topic investigated is the estimation of unitary channels. The situation is considered in which an experimenter has several non-identical unitary channels that have the same parameter. It is shown that it is possible to improve estimation using the channels together, analogous to the case of identical unitary channels. Also, a new method of phase estimation is given based on a method sketched by Kitaev (1996). Unlike other phase estimation procedures which perform similarly, this procedure requires only very basic experimental resources.

Thesis, completed last year

References in corpus (11)

• Simulated Quantum Computation of Molecular Energies
• Entanglement-free Heisenberg-limited phase estimation
• Optimal Quantum Measurements of Expectation Values of Observables
• Qubit metrology and decoherence
• Loss-Induced Limits to Phase Measurement Precision with Maximally Entangled States
• Estimation of unitary quantum operations
• Entanglement is not very useful for estimating multiple phases
• Fast rate estimation of an unitary operation in SU(d)
• Measurement-based quantum phase estimation algorithm for finding eigenvalues of non-unitary matrices
• Asymptotic performance of optimal state estimation in quantum two level system
• Iterative phase estimation