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On Quantum Correlations and Positive Maps

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Abstract

We present a discussion on local quantum correlations and their relations with entanglement. We prove that a vanishing coefficient of quantum correlations implies separability. The new results on locally decomposable maps which we obtain in the course of the proof also seem to be of independent interest.

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References

  1. Alfsen, E.: Compact Convex Sets and Boundary Integrals, Springer-Verlag, New York, 1971.

    Google Scholar 

  2. Bratteli, O. and Robinson, D. W.: Operator Algebras and Quantum Statistical Mechanics, Vol I, Springer-Verlag, New York, 1979.

    Google Scholar 

  3. Horodecki, M. Horodecki, P. and Horodecki, R.: Separability of mixed states: necessary and sufficient conditions, Phys. Lett. A 223 (1996), 1–8.

    Article  ADS  MathSciNet  Google Scholar 

  4. Halmos, P. R.: Finite Dimensional Hilbert Spaces, 2nd edn, D. Van Nostrand, New York, 1958.

    Google Scholar 

  5. Majewski, W. A.: On entanglement of states and quantum correlations, In: J.M. Combes, J. Cuntz, G.A. Elliott, G. Nenciu, H. Siedentop and S. Stratila (eds), Operator Algebras and Mathematical Physics Theta, Bucharest, 2003. e-print, LANL math-ph/0202030.

  6. Majewski, W. A. and Marciniak, M.: On a characterization of positive maps, J. Phys, A.: Math. Gen. 34 (2001), 5863–5874.

    Article  ADS  MathSciNet  Google Scholar 

  7. Peres, A.: Separability criterion for density matrices, Phys. Rev. Lett. 77 (1996), 1413

    ADS  MATH  MathSciNet  Google Scholar 

  8. Størmer, E.: Positive linear maps of operator algebras, Acta Math. 110 (1963), 233–278.

    MATH  MathSciNet  Google Scholar 

  9. Takesaki, M.: Theory of Operator Algebras, Springer-Verlag, Berlin, 1979.

    Google Scholar 

  10. Wittstock, G.: Ordered normed tensor products, In: A. Hartkämper and H. Neumann (eds), Foundations of Quantum Mechanics and Ordered Linear Spaces (Advanced Study Institute held in Marburg), Lecture Notes in Phys. 29, Springer-Verlag, New York, 1974.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Theoretical Physics and Astrophysics, Gdańsk University, Wita Stwosza 57, 80-952, Gdańsk, Poland

    Władysław A. Majewski

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  1. Władysław A. Majewski
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Majewski, W.A. On Quantum Correlations and Positive Maps. Letters in Mathematical Physics 67, 125–132 (2004). https://doi.org/10.1023/B:MATH.0000032702.55066.a6

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  • DOI: https://doi.org/10.1023/B:MATH.0000032702.55066.a6

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