Optimal parameter estimation with a fixed rate of abstention

Abstract

The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or abstention. It is shown that such schemes enable drastic improvements, up to the extent of attaining the Heisenberg limit in some cases, and the required amount of abstention is quantified. A general mathematical framework to deal with the asymptotic limit of many qubits or large angular momentum is introduced and used to obtain analytical results for all the relevant cases under consideration. Parameter estimation with abstention is also formulated as a semidefinite programming problem, for which very efficient numerical optimization techniques exist.

17 pages, 6 figures

References in corpus (5)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Colloquium: Understanding Quantum Weak Values: Basics and Applications
• Information amplification via postselection: A parameter estimation perspective
• State discrimination with error margin and its locality
• Optimal probabilistic estimation of quantum states

Cited by in corpus (9)

• Quantum limits on post-selected, probabilistic quantum metrology
• Optimal quantum operations at zero energy cost
• Programmable discrimination with an error margin
• Probabilistic metrology or how some measurement outcomes render ultra-precise estimates
• Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks
• Probabilistic metrology defeats ultimate deterministic bound
• No-signaling bounds for quantum cloning and metrology
• Ultimate limits of approximate unambiguous discrimination
• Robust Macroscopic Quantum Measurements in the presence of limited control and knowledge