Geodesic
Entanglement measures based on observable correlations
Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 3, pp. 453-462 Cet article a éte moissonné depuis la source Math-Net.Ru

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By regarding quantum states as communication channels and using observable correlations quantitatively expressed by mutual information, we introduce a hierarchy of entanglement measures that includes the entanglement of formation as a particular instance. We compare the maximal and minimal measures and indicate the conceptual advantages of the minimal measure over the entanglement of formation. We reveal a curious feature of the entanglement of formation by showing that it can exceed the quantum mutual information, which is usually regarded as a theoretical measure of total correlations. This places the entanglement of formation in a broader scenario, highlights its peculiarity in relation to pure-state ensembles, and introduces a competing definition with intrinsic informational significance.
Mots-clés : entanglement, observable correlations, entanglement of formation.
Keywords: mutual information 
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S. L. Luo. Entanglement measures based on observable correlations. Teoretičeskaâ i matematičeskaâ fizika, Tome 155 (2008) no. 3, pp. 453-462. http://geodesic.mathdoc.fr/item/TMF_2008_155_3_a4/

[1] A. Einstein, B. Podolsky, N. Rosen, Phys. Rev., 47 (1935), 777–780 | DOI | Zbl

[2] E. Schrödinger, Proc. Camb. Philos. Soc., 31 (1935), 555–563 ; 32 (1936), 446–452 ; Naturwissenchaften, 23 (1935), 807–812 ; 823–828 ; 844–849 | DOI | Zbl | DOI | Zbl | DOI | Zbl | DOI | Zbl

[3] J. S. Bell, Physics, 1 (1964), 195; J. F. Clauser, A. Shimony, Rep. Progr. Phys., 41 (1978), 1881–1927 ; A. Aspect, P. Grangier, G. Roger, Phys. Rev. Lett., 47 (1981), 460–463 | DOI | DOI

[4] M. A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000 | MR | Zbl

[5] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K. Wootters, Phys. Rev. A, 54 (1996), 3824–3851 | DOI | MR

[6] W. K. Wootters, Quantum Inf. Comput., 1 (2001), 27–44 | MR | Zbl

[7] M. Horodecki, Quantum Inf. Comput., 1 (2001), 3–26 | MR | Zbl

[8] C. M. Caves, C. A. Fuchs, P. Rungta, Found. Phys. Lett., 14 (2001), 199–212 | DOI | MR

[9] M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 80 (1998), 5239–5242 | DOI | MR | Zbl

[10] V. Vedral, M. B. Plenio, M. A. Rippin, P. L. Knight, Phys. Rev. Lett., 78 (1997), 2275–2279 ; V. Vedral, M. B. Plenio, Phys. Rev. A, 57 (1998), 1619–1633 | DOI | MR | Zbl | DOI

[11] G. Vidal, R. F. Werner, Phys. Rev. A, 65 (2002), 032314 | DOI

[12] M. Christandl, A. Winter, J. Math. Phys., 45 (2004), 829–840 | DOI | MR | Zbl

[13] P. W. Shor, Comm. Math. Phys., 246 (2004), 453–472 | DOI | MR | Zbl

[14] H. Everett III, “The theory of the universal wavefunction”, The Many-Worlds Interpretation of Quantum Mechanics, eds. B. S. DeWitt, N. Graham, Princeton University Press, Princeton, 1973, 3

[15] C. E. Shannon, Bell System. Tech. J., 27 (1948), 379–423 ; 623–656 | DOI | MR | Zbl

[16] T. M. Cover, J. A. Thomas, Elements of Information Theory, Wiley, New York, 1991 | MR | Zbl

[17] B. Schumacher, “Information from quantum measurements”, Complexity, Entropy and the Physics of Information, Proc. Workshop (St. John's College, Santa Fe, New Mexico, May 29–June 2, 1989), Santa Fe Institute Studies in the Sciences of Complexity, VIII, ed. W. H. Zurek, Addison-Wesley, Redwood City, CA, 1990, 29 | MR

[18] R. Jozsa, D. Robb, W. K. Wootters, Phys. Rev. A, 49 (1994), 668–677 | DOI | MR

[19] A. S. Kholevo, Problems Inform. Transmission, 15:4 (1979), 247–253 | MR | Zbl

[20] V. Vedral, Rev. Modern. Phys., 74 (2002), 197–234 | DOI | MR | Zbl

[21] S. Popescu, D. Rorhlich, Phys. Rev. A, 56 (1997), R3319–R3321 | DOI | MR

[22] R. F. Werner, Phys. Rev. A, 40 (1989), 4277–4281 | DOI

[23] K. G. H. Vollbrecht, R. F. Werner, Phys. Rev. A, 64 (2001), 062307 | DOI

[24] C. Adami, N. J. Cerf, Phys. Rev. A, 56 (1997), 3470–3483 ; L. Henderson, V. Vedral, J. Phys. A, 34 (2001), 6899–6905 ; H. Ollivier, W. H. Zurek, Phys. Rev. Lett., 88 (2002), 017901 ; B. Groisman, S. Popescu, A. Winter, Phys. Rev. A, 72 (2005), 032317 ; B. Schumacher, M. D. Westmoreland, Phys. Rev. A, 74 (2006), 042305 | DOI | MR | DOI | MR | Zbl | DOI | Zbl | DOI | MR | DOI

[25] G. Vidal, J. Modern. Opt., 47 (2000), 355–376 | MR

[26] M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett., 84 (2000), 2014–2017 | DOI | MR

[27] P. M. Hayden, M. Horodecki, B. M. Terhal, J. Phys. A, 34 (2001), 6891–6898 | DOI | MR | Zbl

[28] N. Li, S. Luo, Phys. Rev. A, 76 (2001), 032327 | DOI