Qubit representation of qudit states: correlations and state reconstruction

  • Julio A. López-SaldívarEmail author
  • Octavio Castaños
  • Margarita A. Man’ko
  • Vladimir I. Man’ko


A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the qudit state imply the existence of quantum correlations between the qubits which compose it. These correlations are used to define new inequalities which the density matrices components must satisfy. The importance of such inequalities in the reconstruction of a qudit state is addressed. As an example of the general procedure, the qubit decomposition of a qutrit system is shown, which allows a classification of the qutrit states by fixing their invariants \(\mathrm{Tr}(\hat{\rho }^2)\), \(\mathrm{Tr}(\hat{\rho }^3)\).


Qudit states Geometrical representation of quantum states Quantum correlations Quantum state reconstruction Bloch sphere 



This work was partially supported by DGAPA-UNAM (Under Project IN101619).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Julio A. López-Saldívar
    • 1
    • 2
    Email author
  • Octavio Castaños
    • 1
  • Margarita A. Man’ko
    • 3
  • Vladimir I. Man’ko
    • 2
    • 3
    • 4
  1. 1.Instituto de Ciencias NuclearesUniversidad Nacional Autnoma de MexicoCDMXMexico
  2. 2.Moscow Institute of Physics and Technology (State University)Dolgoprudnyi, Moscow RegionRussia
  3. 3.Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia
  4. 4.Department of PhysicsTomsk State UniversityTomskRussia

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