Erratum: Sufficient conditions for three-particle entanglement and their tests in recent experiments (Physical Review A (2005) 72:1 (014101))

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 72, Issue 1, 2005, Pages

  Toth, Geza ^a   Guhne, Otfried ^b   Seevinck, Michael ^c   Uffink, Jos ^c  

^a MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^b ERICH SCHMID INSTITUTE OF MATERIALS SCIENCE   (Austria)

^c UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27144516460     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.72.014101     Document Type: Erratum

References (13)

1. M. Seevinck and J. Uffink, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.012107 65, 012107 (2002).
2. Consequently, a mixed state is called biseparable (fully separable) if it is the mixture of pure biseparable (fully separable) states.
3. N. D. Mermin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65. 1838 65, 1838 (1990).
4. For a different proof see Geza Toth and Otfried Guhne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.060501 94, 060501 (2005);
5. Geza Toth and Otfried Guhne, quant-ph/0501020.
6. N. Gisin and H. Bechmann-Pasquinucci, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(98)00516-7 246, 1 (1998).
7. D. Collins, N. Gisin, S. Popescu, D. Roberts, and V. Scarani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.170405 88, 170405 (2002).
8. J.-W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, Nature (London) NATUAS 0028-0836 10.1038/35000514 403, 515 (2000);
9. see also p. 209 of D. Bouwmeester, A. Ekert and Z. Zeilinger, The Physics of Quantum Information (Springer, Berlin, 2000).
10. This can be proved as follows. Let us take 8 to be a 4-4 matrix in the usual Z(k) basis, with matrix elements 8 kl with k,l=1,2,3,4. Then 88\'a3\parv1'e2\'88\'a32=('e2\'9f\'a8X(1)X(2)'e2\'88\rquote Y(1)Y(2)'e2\'9f\'a9\ 'cf\'81)2+('e2\'9f\'a8X(1)Y(2)+Y(1)X(2)'e2\'9f\'a9\'cf\'81)2=16'cf\'8114'cf\ '8141'e2\'a9\'bd4. The last inequality is valid since 'e2\'88\'a3'cf\'8114'e2\ '88\'a3=\'e2\'88\'a3'cf\'8141'e2\'88\'a3'e2\'a9\'bd1 2 is required for physically meaningful density matrices. See also Eq. (3) of J. Uffink, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.230406 88, 230406 (2002).
11. We note that in a long calculation using the fidelity criterion, K. Nagata, M. Koashi, and N. Imoto, proved that the experiment contained three-particle entanglement but without using the Mermin inequality: K. Nagata, M. Koashi, and N. Imoto, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65. 042314 65, 042314 (2002);
12. as we have recently been informed in a calculation different from ours, K. Nagata, M. Koashi, and N. Imoto, also obtained the here presented bound for the Mermin inequality in an unpublished work to be found at http://www.qci.jst. go.jp/eqis02/program/abstract/poster11.pdf.
13. The bound, while not explicitly stated, can straightforwardly be obtained from K. Nagata, M. Koashi, and N. Imoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.260401 89, 260401 (2002).