Research PaperNo Access

Full-separability and bi-separability of qubits using Bell operators, partial transpose, witnesses and explicit (full/bi) separability

Y. Ben-Aryeh

Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel

E-mail Address: phr65yb@physics.technion.ac.il

Corresponding author.

Search for more papers by this author

and

A. Mann

Physics Department, Technion-Israel Institute of Technology, Haifa 32000, Israel

E-mail Address: ady@physics.technion.ac.il

Search for more papers by this author

https://doi.org/10.1142/S0219749922500113Cited by:0 (Source: Crossref)

Abstract

Using the Hilbert–Schmidt (HS) decomposition we suggest new possible choices of Bell operators and entanglement witnesses (EWs) for $n$ ( $> 2$ ) qubits systems for (full/bi) separability. The latter give upper bounds for (full/bi) separability. Also using the HS decomposition, we find explicitly (full/bi) separable forms for some qubits states which give lower bounds for (full/bi) separability. When the lower bounds and upper bounds coincide it means that the EW is optimal. In the case of full separability, the positive transpose method can sometimes give optimal results. As concrete examples, we give results for the GHZ(3), $W (3)$ and cluster $C l (4)$ states.

Keywords:

References

1. A. Peres, Phys. Rev. Lett. 77 (1996) 1413. Crossref, Web of Science, Google Scholar
2. M. Horodecki and P. Horodecki, Phys. Lett. A 223 (1996) 1. Crossref, Web of Science, Google Scholar
3. J.-D. Bancal et al., Phys. Rev. Lett. 106 (2011) 250404. Crossref, Web of Science, Google Scholar
4. R. Y. Teh and M. D. Reid, Phys. Rev. A 90 (2014) 062337. Crossref, Web of Science, Google Scholar
5. Y. Ben-Aryeh and A. Mann, Int. J. Quantum Inf. 14 (2016) 1650044. Link, Web of Science, Google Scholar
6. R. Horodecki and M. Horodecki, Phys. Rev. A 54 (1996) 1838. Crossref, Web of Science, Google Scholar
7. Y. Ben-Aryeh and A. Mann, Int. J. Quantum Inf. 14 (2016) 1650030. Link, Web of Science, Google Scholar
8. Y. Ben-Aryeh and A. Mann, J. Phys. Commun. 2 (2018) 125011. Crossref, Google Scholar
9. J. F. Clauser et al., Phys. Rev. Lett. 23 (1969) 880. Crossref, Web of Science, Google Scholar
10. S. L. Braunstein et al., Phys. Rev. Lett. 68 (1992) 3259. Crossref, Web of Science, Google Scholar
11. D. N. Klyshko, Phys. Lett. A 172 (1993) 399. Crossref, Web of Science, Google Scholar
12. N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A 246 (1998) 1. Crossref, Web of Science, Google Scholar
13. M. Zukowski and C. Brukner, Phys. Rev. Lett. 88 (2002) 210401. Crossref, Web of Science, Google Scholar
14. R. Horodecki and P. Horodecki, Phys. Lett. A 210 (1996) 227. Crossref, Web of Science, Google Scholar
15. A. Cabello, Phys. Rev. A 65 (2002) 032108. Crossref, Web of Science, Google Scholar
16. B. M. Terhal, Phys. Lett. A 271 (2000) 319. Crossref, Web of Science, Google Scholar
17. B. M. Terhal, Theor. Compu. Sci. 287 (2002) 313. Crossref, Web of Science, Google Scholar
18. O. Guhne and P. Hyllus, Int. J. Theor. Phys. 42 (2003) 1001. Crossref, Web of Science, Google Scholar
19. P. Hyllus et al., Phys. Rev. A 72 (2005) 012321. Crossref, Web of Science, Google Scholar
20. O. Guhne and G. Toth, Phys. Rep. 474 (2009) 1. Crossref, Web of Science, Google Scholar
21. O. Guhne et al., Phys. Rev. A 66 (2002) 062305. Crossref, Web of Science, Google Scholar
22. A. Sanpera et al., Phys. Rev. A 63 (2001) 050301(R). Crossref, Web of Science, Google Scholar
23. M. Bourennane et al., Phys.Rev. Lett. 92 (2004) 087902. Crossref, Web of Science, Google Scholar
24. S.-H. Kye, J. Phys. A:Math. Theor. 48 (2015) 235303. Crossref, Web of Science, Google Scholar
25. M. Huber and R. Sengupta, Phys. Rev. Lett. 113 (2014) 100501. Crossref, Web of Science, Google Scholar
26. K. Nagata et al., Int. J. Theor. Phys. 57 (2018) 2116. Crossref, Web of Science, Google Scholar
27. J. T. Barreiro et al., Nat. Phys. 9 (2013) 559. Crossref, Web of Science, Google Scholar
28. O. Guhne and M. Seevinck, New J. Phys. 12 (2010) 053002. Crossref, Web of Science, Google Scholar
29. D. Bruss, J. Math. Phys. 43 (2002) 4237. Crossref, Web of Science, Google Scholar
30. N. D. Mermin, Phys. Rev. Lett. 65 (1990) 1838. Crossref, Web of Science, Google Scholar
31. Y. Ben-Aryeh and A. Mann, Int. J. Quantum Inf. 13 (2015) 1550061. Link, Web of Science, Google Scholar
32. R. Schack and C. M. Caves, J. Mod. Opt. 47 (2000) 387. Crossref, Web of Science, Google Scholar
33. W. Dur et al., Phys. Rev. A 62 (2000) 062314. Crossref, Web of Science, Google Scholar
34. A. Acin et al., Phys. Rev. Lett. 87 (2001) 040401. Crossref, Web of Science, Google Scholar
35. S. Szalay, Phys. Rev. A 83 (2011) 062337. Crossref, Web of Science, Google Scholar