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

2013/01/31 by Elisa Ercolessi, Michele Schiavina · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #math-ph #math.MP #msc:81Q70 #msc:81R05 #msc:81S10 #quant-ph

paper · pdf · doi:10.1016/j.physleta.2013.06.012

published as Physics Letters A, Volume 377, Issues 34-36, 1 November 2013, Pages 1996-2002 · Final published version, minor changes

openalex publication_date 2013/06/14 · arxiv created 2013/07/16 · arxiv updated 2013/07/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

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), 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.

Citations

• General setting for a geometric phase of mixed states under an arbitrary nonunitary evolution
• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Maximum Fisher information in mixed state quantum systems
• Quantal phase factors accompanying adiabatic changes
• Geometric Quantum Mechanics

Cited by

• Tomographic reconstruction of quantum metrics
• A pedagogical intrinsic approach to relative entropies as potential functions of quantum metrics: Theq–zfamily
• Quantum Fisher information and symmetric logarithmic derivative via anti-commutators

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• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
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