Non-Orthogonal Bases for Quantum Metrology

Genoni, Marco G.; Tufarelli, Tommaso

Abstract

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.

Citation

Genoni, M. G., & Tufarelli, T. (2019). Non-Orthogonal Bases for Quantum Metrology. Journal of Physics A: Mathematical and Theoretical, 52(43), 1-18. https://doi.org/10.1088/1751-8121/ab3fe0

• 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
• DOI: https://doi.org/10.1088/1751-8121/ab3fe0
• Keywords: Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/2591057
• Publisher URL: https://iopscience.iop.org/article/10.1088/1751-8121/ab3fe0
• Contract Date: Sep 9, 2019