Group theoretic structures in the estimation of an unknown unitary transformation

Abstract

This paper presents a series of general results about the optimal estimation of physical transformations in a given symmetry group. In particular, it is shown how the different symmetries of the problem determine different properties of the optimal estimation strategy. The paper also contains a discussion about the role of entanglement between the representation and multiplicity spaces and about the optimality of square-root measurements.

15 pages, lecture given at The XXVIII International Colloquium on Group-Theoretical Methods in Physics, 26-30 July 2010, Newcastle upon Tyne (UK)

References in corpus (5)

• Reference frames, superselection rules, and quantum information
• Beating the Standard Quantum Limit with Four Entangled Photons
• Entanglement-free Heisenberg-limited phase estimation
• Probabilistic theories with purification
• Design of Optimal Dynamic Analyzers: Mathematical Aspects of Wave Pattern Recognition

Cited by in corpus (5)

• Quantum Theory, namely the pure and reversible theory of information
• Units of rotational information
• Fourier Analytic Approach to Quantum Estimation of Group Action
• Phase-asymmetry resource interconversion via estimation
• Indefinite causal order strategy does not improve the estimation of group action