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Non-Orthogonal Bases for Quantum Metrology

Genoni, Marco G.; Tufarelli, Tommaso


Marco G. Genoni


Many quantum statistical models are most conveniently formulated in terms of non-orthonormal bases. This is the case, for example, when mixtures and superpositions of coherent states are involved. In these instances, we show that the analytical evaluation of the quantum Fisher information matrix may be greatly simplified by bypassing both the diagonalization of the density matrix and the orthogonalization of the basis. The key ingredient in our method is the Gramian matrix (i.e. the matrix of scalar products between basis elements), which may be interpreted as a metric tensor for index contraction. As an application, we derive novel analytical results for several estimation problems involving noisy Schrödinger cat states.


Genoni, M. G., & Tufarelli, T. (2019). Non-Orthogonal Bases for Quantum Metrology. Journal of Physics A: Mathematical and Theoretical, 52(43), 1-18.

Journal Article Type Article
Acceptance Date Aug 30, 2019
Online Publication Date Aug 30, 2019
Publication Date Oct 1, 2019
Deposit Date Sep 9, 2019
Publicly Available Date Sep 9, 2019
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 52
Issue 43
Pages 1-18
Keywords Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
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