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Advances in Mathematical Physics
Volume 2012 (2012), Article ID 104856, 6 pages
http://dx.doi.org/10.1155/2012/104856
Research Article

The Entanglement of Independent Quantum Systems

Shuilin Jin1 and Li Xu2

1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2College of Computer Science and Technology, Harbin Engineering University, Harbin 150001, China

Received 1 November 2012; Accepted 18 December 2012

Academic Editor: Shao-Ming Fei

Copyright © 2012 Shuilin Jin and Li Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Bruß, “Characterizing entanglement,” Journal of Mathematical Physics, vol. 43, no. 9, pp. 4237–4251, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. P. Caban, K. Podlaski, J. Rembieliński, K. A. Smoliński, and Z. Walczak, “Entanglement and tensor product decomposition for two fermions,” Journal of Physics A, vol. 38, no. 6, pp. L79–L86, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Miyake, “Classification of multipartite entangled states by multidimensional determinants,” Physical Review A, vol. 67, no. 1, Article ID 012108, 10 pages, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. H. Moriya, “Some aspects of quantum entanglement for CAR systems,” Letters in Mathematical Physics, vol. 60, no. 2, pp. 109–121, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X.-W. Hou, J.-H. Chen, M.-F. Wan, and Z.-Q. Ma, “Entropy correlation and entanglement for mixed states in an algebraic model,” Journal of Physics A, vol. 42, no. 7, Article ID 075301, 10 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  6. E. Karimi, J. Leach, S. Slussarenko et al., “Spin-orbit hybrid entanglement of photons and quantum contextuality,” Physical Review A, vol. 82, Article ID 022115, 2010. View at Google Scholar
  7. F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Physical Review A, vol. 82, Article ID 052118, 2010. View at Google Scholar
  8. S. Luo and Q. Zhang, “On skew information,” IEEE Transactions on Information Theory, vol. 50, no. 8, pp. 1778–1782, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Luo and Q. Zhang, “Observable correlations in two-qubit states,” Journal of Statistical Physics, vol. 136, no. 1, pp. 165–177, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. S. L. Luo, N. Li, and X. L. Cao, “Relation between “no broadcasting” for noncommuting states and “no local broadcasting” for quantum correlations,” Physical Review A, vol. 79, Article ID 054305, 2009. View at Google Scholar
  11. R. Vasile, P. Giorda, S. Olivares, M. G. A. Paris, and S. Maniscalco, “Non-classical correlations in non-Markovian continuous-variable systems,” Physical Review A, vol. 82, Article ID 012313, 2010. View at Google Scholar
  12. R. Haag and D. Kastler, “An algebraic approach to quantum field theory,” Journal of Mathematical Physics, vol. 5, pp. 848–861, 1964. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Roos, “Independence of local algebras in quantum field theory,” Communications in Mathematical Physics, vol. 16, pp. 238–246, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Florig and S. J. Summers, “On the statistical independence of algebras of observables,” Journal of Mathematical Physics, vol. 38, no. 3, pp. 1318–1328, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. J. Bunce and J. Hamhalter, “C∗-independence, product states and commutation,” Annales Henri Poincaré, vol. 5, no. 6, pp. 1081–1095, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. M. Zhang and S. L. Jin, “Characterization of quantum independence by joint numerical range,” Journal of Jilin University, vol. 48, no. 2, pp. 234–236, 2010. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. L. Jin, L. Xu, Q. H. Jiang, and G. R. Duan, “A joint spectral characterization of C∗ independence,” Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 15, no. 2, Article ID 1250013, 2012. View at Google Scholar
  18. S. L. Jin, L. Xu, Q. H. Jiang, and L. Li, “Conditions equivalent to C∗ independence,” Studia Mathematica, pp. 191–197, 2012. View at Google Scholar
  19. W. Żelazko, Banach Algebras, Elsevier, New York, NY, USA, 1973. View at MathSciNet
  20. P. Juneja, “On extreme points of the joint numerical range of commuting normal operators,” Pacific Journal of Mathematics, vol. 67, no. 2, pp. 473–476, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet