QLunch: Elias Theil
Speaker: Elias Theil
Title: Quantum purity amplification and coherent inference theory
Abstract: When given access to multiple copies of a noisy quantum state, we might want to extract the underlying pure state for further processing. This task is called quantum purity amplification (QPA). A naive approach to QPA would be to perform state tomography, and then prepare the pure eigenstate with the largest eigenvalue, which incurs an error O(d/n), where d is the dimension of the state and n the number of copies available. If we instead process the inputs in a coherent way, i.e. without measuring them, we can achieve an error of O(1/n).
In my presentation, I will talk about an asymptotically optimal protocol for QPA, together with tight bounds on the resulting fidelities. This protocol also works for the more general case of eigenstate extraction, where we want to obtain an arbitrary eigenstate instead of the one with largest eigenvalue. Finally, I will talk about the general idea of coherent inference theory, which provides a framework for problems where you want to extract information from a quantum state in a coherent manner.