Quantum Information Processing

, Volume 10, Issue 4, pp 431–447 | Cite as

Tractable measure of nonclassical correlation using density matrix truncations

  • Akira SaiToh
  • Robabeh Rahimi
  • Mikio Nakahara


In the context of the Oppenheim-Horodecki paradigm of nonclassical correlation, a bipartite quantum state is (properly) classically correlated if and only if it is represented by a density matrix having a product eigenbasis. On the basis of this paradigm, we propose a measure of nonclassical correlation by using truncations of a density matrix down to individual eigenspaces. It is computable within polynomial time in the dimension of the Hilbert space albeit imperfect in the detection range. This is in contrast to the measures conventionally used for the paradigm. The computational complexity and mathematical properties of the proposed measure are investigated in detail and the physical picture of its definition is discussed.


Nonclassical correlation Quantumness Computational tractability Informational entropy Matrix truncation 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Akira SaiToh
    • 1
  • Robabeh Rahimi
    • 2
    • 3
  • Mikio Nakahara
    • 1
    • 4
  1. 1.Research Center for Quantum Computing, Interdisciplinary Graduate School of Science and EngineeringKinki UniversityOsakaJapan
  2. 2.Departments of Chemistry and Materials Science, Graduate School of ScienceOsaka City UniversityOsakaJapan
  3. 3.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada
  4. 4.Department of PhysicsKinki UniversityOsakaJapan

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