Maximum likelihood estimation for a group of physical transformations

Abstract

The maximum likelihood strategy to the estimation of group parameters allows to derive in a general fashion optimal measurements, optimal signal states, and their relations with other information theoretical quantities. These results provide a deep insight into the general structure underlying optimal quantum estimation strategies. The entanglement between representation spaces and multiplicity spaces of the group action appear to be the unique kind of entanglement which is really useful for the optimal estimation of group parameters.

20 pages, no figures. World Scientific class style. Contribution for the Proceedings of the Workshop on "Quantum entanglement in physical and information sciences", held in Pisa, December 14-18, 2004

References in corpus (8)

• Classical and quantum communication without a shared reference frame
• Efficient use of quantum resources for the transmission of a reference frame
• Optimal estimation of group transformations using entanglement
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Quantum reverse-engineering and reference frame alignment without non-local correlations
• Covariant quantum measurements which maximize the likelihood
• Entanglement assisted alignment of reference frames using a dense covariant coding
• Optimal phase estimation for qubit mixed states

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• Quantum communication using a bounded-size quantum reference frame
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• Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
• Unsupervised classification of quantum data
• Optimal Measurements for Symmetric Quantum States with Applications to Optical Communication
• Quantifying quantum reference frames in composed systems: local, global and mutual asymmetries
• Identification of a reversible quantum gate: assessing the resources
• Fourier Analytic Approach to Quantum Estimation of Group Action
• Group theoretic structures in the estimation of an unknown unitary transformation
• Optimal asymptotic cloning machines
• A generalized wave-particle duality relation for finite groups
• Relativistic quantum information theory and quantum reference frames
• Causality in Higher Order Process Theories
• Robust Macroscopic Quantum Measurements in the presence of limited control and knowledge