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A Triality Pattern in Entanglement Theory Cover
By: Daniel Cariello  
Open Access
|Nov 2024

References

  1. O. Gühne and G. Tóth (2009). “Entanglement detection”. Physics Reports, 474: 1–6, 1–75.
  2. A. Peres (1996). “Separability criterion for density matrices”. Physical Review Letters, 77: 8, 1413.
  3. M. Horodecki, P. Horodecki and R. Horodecki (1996). “Separability of mixed states: Necessary and sufficient conditions”. Physics Letters A, 223, 1–8.
  4. L. Gurvits (2004). “Classical complexity and quantum entanglement”. Journal of Computer and System Sciences, 69: 3, 448–484.
  5. D. Cariello (2016). “Completely reducible maps in quantum information theory”. IEEE Transactions on Information Theory, 62: 4, 1721–1732.
  6. G. Tóth and O. Gühne (2010). “Separability criteria and entanglement witnesses for symmetric quantum states”. Applied Physics B, 98: 4, 617–622.
  7. M. Horodecki, P. Horodecki and R. Horodecki (2006). “Separability of mixed quantum states: Linear contractions approach”. Open Systems & Information Dynamics, 13, 103.
  8. O. Rudolph (2005). “Computable cross-norm criterion for separability”. Letters in Mathematical Physics, 70, 57–64.
  9. O. Rudolph (2005). “Further results on the cross norm criterion for separability”. Quantum Information Processing, 4, 219–239.
  10. J.M. Leinaas, J. Myrheim and E. Ovrum (2006). “Geometrical aspects of entanglement”. Physical Review A, 74: 3, 012313.
  11. W. Dür, G. Vidal and J.I. Cyrac (2002). “Optimal conversion of nonlocal unitary operations”. Physical Review Letters, 89: 5, 057901.
  12. B. Kraus and J.I. Cyrac (2001). “Optimal creation of entanglement using a two-qubit gate”. Physical Review A, 63: 6, 062309.
  13. O. Gittsovich, O. Gühne, P. Hyllus and J. Eisert (2008). “Unifying several separability conditions using the covariance matrix criterion”. Physical Review A, 78, 052319.
  14. P. Horodecki, M. Lewenstein, G. Vidal and I. Cirac (2000). “Operational criterion and constructive checks for the separability of low-rank density matrices”. Physical Review A, 62: 3, 032310.
  15. P. Horodecki, J.A. Smolin, B.M. Terhal and A.V. Thapliyal (2003). “Rank two bipartite bound entangled states do not exist”. Theoretical Computer Science, 292: 3, 589–596.
  16. C.-K. Li, Y.-T. Poon and X. Wang (2014). “Ranks and eigenvalues of states with prescribed reduced states”. Electronic Journal of Linear Algebra, 27, 935–950.
  17. H. Chen (2003). “Schmidt numbers of low-rank bipartite mixed states”. Physical Review A, 67: 6, 062301.
  18. E.P. Hanson, C. Rouzé and D. Stilck França (2020). “Eventually entanglement breaking markovian dynamics: Structure and characteristic times”. Annales Henri Poincaré, 21, 1517–1571.
  19. M. Weiner (2013). “A gap for the maximum number of mutually unbiased bases”. Proceedings of the American Mathematical Society, 141: 6, 1963–1969.
  20. D. Cariello (2014). “Separability for weakly irreducible matrices”. Quantum Information & Computation, 14: 15–16, 1308–1337.
  21. D. Cariello (2019). “Sinkhorn-Knopp theorem for rectangular positive maps”. Linear and Multilinear Algebra, 67, 2345–2365.
  22. M. Marcus and H. Minc (1992). A Survey of Matrix Theory and Matrix Inequalities, volume 14, Courier Corporation.
  23. R. Sinkhorn and P. Knopp (1967). “Concerning nonnegative matrices and doubly stochastic matrices”. Pacific Journal of Mathematics, 21: 2, 343–348.
  24. R. Bhatia (2009). Positive Definite Matrices, Princeton University Press.
DOI: https://doi.org/10.2478/qic-2024-0003 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
Language: English
Page range: 40 - 57
Submitted on: Sep 6, 2024
Accepted on: Nov 13, 2024
Published on: Nov 25, 2024
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2024 Daniel Cariello, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License.