Non-commutative measure of quantum correlations under local operations

  • D. G. Bussandri
  • A. P. Majtey
  • A. Valdés-HernándezEmail author


We study some desirable properties of recently introduced measures of quantum correlations based on the amount of non-commutativity quantified by the Hilbert–Schmidt norm (Guo in Sci Rep 6:25241, 2016; Majtey et al. in Quantum Inf Process 16:226, 2017). Specifically, we show that: (1) for any bipartite (\(A+B\)) state, the measures of quantum correlations with respect to subsystem A are non-increasing under any local commutative preserving operation on subsystem A, and (2) for Bell-diagonal states, the measures are non-increasing under arbitrary local operations on B. Our results accentuate the potentialities of such measures and exhibit them as valid monotones in a resource theory of quantum correlations with free operations restricted to the appropriate local channels.


Quantum correlation measures Non-commutativity quantum discord Local operations Local commutative preserving operations 



D. B. and A. P. M. acknowledge the Argentinian agency SeCyT-UNC and CONICET for financial support. D. B. has a fellowship from CONICET. A. V. H. gratefully acknowledges financial support from DGAPA, UNAM through project PAPIIT IA101918.


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Authors and Affiliations

  1. 1.Facultad de Matemática, Astronomía, Física y ComputaciónUniversidad Nacional de CórdobaCórdobaArgentina
  2. 2.Consejo Nacional de Investigaciones Científicas y Técnicas de la República ArgentinaCABAArgentina
  3. 3.Instituto de Física Enrique GaviolaConsejo Nacional de Investigaciones Científicas y Técnicas de la República ArgentinaCórdobaArgentina
  4. 4.Instituto de FísicaUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

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