2017/04/30 by Marco Laudato, G. Marmo, Giuseppe Marmo +4 · 9 citations
Mathematics · Physics and Astronomy · #Bijection #Discrete mathematics #Geometry #Mathematical Analysis and Transform Methods #Mathematics #Metric (unit) #Metric space #Monotone polygon #Numerical methods in inverse problems #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1751-8121/aa9e61
published in Journal of Physics A Mathematical and Theoretical 51(5), 055302 (Institute of Physics) · v1:19 pages, 2 figures. Abstract modified, references added, minor corrections. v2:Revised versione accepted for publication
arxiv created 2017/11/29 · openalex publication_date 2017/11/30 · arxiv updated 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme is chosen, and monotone quantum metrics on the space of quantum states, classified by operator monotone functions, according to the Petz classification theorem. We show that different metrics can be related through a change in the tomographic map and prove that there exists a bijective relation between monotone quantum metrics associated with different operator monotone functions. Such a bijective relation is uniquely defined in terms of solutions of a first order second degree differential equation for the parameters of the involved tomographic maps. We first exhibit an example of a non-linear tomographic map that connects a monotone metric with a new one, which is not monotone. Then we provide a second example where two monotone metrics are uniquely related through their tomographic parameters.