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Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems


Ercolessi, E; Schiavina, M (2013). Symmetric logarithmic derivative for general n-level systems and the quantum Fisher information tensor for three-level systems. Physics Letters A, 377(34-36):1996-2002.

Abstract

Within a geometrical context, we derive an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two-level mixed and three-level pure state systems and then apply it to the novel case of U(3)U(3), that is for arbitrarily mixed three-level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a q-trit considering also all possible degenerate subcases.

Abstract

Within a geometrical context, we derive an explicit formula for the computation of the symmetric logarithmic derivative for arbitrarily mixed quantum systems, provided that the structure constants of the associated unitary Lie algebra are known. To give examples of this procedure, we first recover the known formulae for two-level mixed and three-level pure state systems and then apply it to the novel case of U(3)U(3), that is for arbitrarily mixed three-level systems (q-trits). Exploiting the latter result, we finally calculate an expression for the Fisher tensor for a q-trit considering also all possible degenerate subcases.

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5 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Quantum Fisher information; Symmetric logarithmic derivative; Unitary group; Fisher tensor
Language:English
Date:2013
Deposited On:23 Jul 2013 14:06
Last Modified:07 Dec 2017 21:29
Publisher:Elsevier
ISSN:0375-9601
Publisher DOI:https://doi.org/10.1016/j.physleta.2013.06.012
Related URLs:http://arxiv.org/abs/1301.6500

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