Inequalities for quantum skew information

Koenraad Audenaert, Liang Cai, Frank Hansen

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


We study quantum information inequalities and show that the basic inequality between the quantum variance and the metric adjusted skew information generates all the multi-operator matrix inequalities or Robertson type determinant inequalities studied by a number of authors. We introduce an order relation on the set of functions representing quantum Fisher information that renders the set into a lattice with an involution. This order structure generates new inequalities for the metric adjusted skew informations. In particular, the Wigner-Yanase skew information is the maximal skew information with respect to this order structure in the set of Wigner-Yanase-Dyson skew informations.

Original languageEnglish
Pages (from-to)135-146
Number of pages12
JournalLetters in Mathematical Physics
Issue number2-3
Publication statusPublished - 2008 Sep
Externally publishedYes


  • Metric adjusted skew information
  • Operator monotone function
  • Quantum covariance
  • Robertson-type uncertainty principle
  • Wigner-Yanase-Dyson skew information.

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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