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 chosen, and monotone quantum metrics on the space of quantum states, classified by operator monotone functions, according to Petz classification theorem. We show that different metrics can be related through a change of the tomographic map and prove that there exists a bijective relation between monotone quantum metrics associated with different operator monotone functions. Such 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 which 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.

Tomographic reconstruction of quantum metrics / Laudato, Marco; Marmo, Giuseppe; Mele, Fabio M.; Ventriglia, Franco; Vitale, Patrizia. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 51:5(2018), p. 055302. [10.1088/1751-8121/aa9e61]

Tomographic reconstruction of quantum metrics

Marmo, Giuseppe
Investigation
;
Ventriglia, Franco
Investigation
;
Vitale, Patrizia
Investigation
2018

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 chosen, and monotone quantum metrics on the space of quantum states, classified by operator monotone functions, according to Petz classification theorem. We show that different metrics can be related through a change of the tomographic map and prove that there exists a bijective relation between monotone quantum metrics associated with different operator monotone functions. Such 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 which 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.
2018
Tomographic reconstruction of quantum metrics / Laudato, Marco; Marmo, Giuseppe; Mele, Fabio M.; Ventriglia, Franco; Vitale, Patrizia. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 51:5(2018), p. 055302. [10.1088/1751-8121/aa9e61]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/710701
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