Year: 2023
Type: preprint
Abstract: We study Haar-random bases and pretty good measurement for Bayesian state estimation. Given $N$ Haar-random bases we derive a bound on fidelity averaged over IID sequences of such random measurements for a uniform ensemble of pure states. For ensembles of mixed qubit states, we find that measurements defined through unitary 2-designs closely approximate those defined via Haar random unitaries while the Pauli group only gives a weak lower bound. For a single-shot-update, we show using the Petz recovery map for pretty good measurement that it can give pretty good Bayesian mean estimates.
Source: arXiv (Cornell University)
Author: Quadeer, Maria
Institution: Nanyang Technological University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Nanyang Technological University
OpenAlex ID: W4388184948