Geodesic
Probability representation of spin states and inequalities for unitary matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 151-161 Cet article a éte moissonné depuis la source Math-Net.Ru

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We review the probability representation of spin states described by probability distributions (tomograms). We use the relation of a tomogram to unitary group elements to obtain some inequalities for unitary matrices. We present the Cirel'son bound and the entropic inequalities for entangled spin states in the form of relations for functions on the unitary group.
Mots-clés : entanglement
Keywords: tomographic probability, Bell's inequality, entropic uncertainty relation. 
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M. A. Man'ko. Probability representation of spin states and inequalities for unitary matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 1, pp. 151-161. http://geodesic.mathdoc.fr/item/TMF_2011_168_1_a11/

[1] S. Mancini, V. I. Man'ko, P. Tombesi, Phys. Lett. A, 213:1–2 (1996), 1–6, arXiv: quant-ph/9603002 | DOI | MR | Zbl

[2] S. Mancini, V. I. Man'ko, P. Tombesi, Found. Phys., 27:6 (1997), 801–824, arXiv: quant-ph/9609026 | DOI | MR

[3] V. V. Dodonov, V. I. Man'ko, Phys. Lett. A, 229:6 (1997), 335–339 | DOI | MR | Zbl

[4] V. I. Manko, O. V. Manko, ZhETF, 112:3 (1997), 430–434 | DOI

[5] A. Ibort, V. I. Man'ko, G. Marmo, A. Simoni, F. Ventriglia, Phys. Scr., 79:6 (2009), 065013, 29 pp., arXiv: 0904.4439 | DOI | Zbl

[6] D. T. Smithey, M. Beck, M. G. Raymer, A. Faridani, Phys. Rev. Lett., 70:9 (1993), 1244–1247 | DOI

[7] G. Breitenbach, S. Schiller, J. Mlynek, Nature, 387:6632 (1997), 471–475 | DOI

[8] E. Wigner, Phys. Rev., 40:5 (1932), 749–759 | DOI

[9] J. Bertrand, P. Bertrand, Found. Phys., 17:4 (1987), 397–405 | DOI | MR

[10] K. Vogel, H. Risken, Phys. Rev. A, 40:5 (1989), 2847–2849 | DOI

[11] E. Schrödinger, Proc. Cambridge Philos. Soc., 31:4 (1935), 555–563 | DOI

[12] V. A. Andreev, V. I. Manko, O. V. Manko, E. V. Schukin, TMF, 146:1 (2006), 172–185 | DOI | MR | Zbl

[13] M. A. Manko, V. I. Manko, TMF, 160:1 (2009), 143–156, arXiv: 0902.4381 | DOI | MR | Zbl

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

[15] A. Rényi, Probability Theory, North-Holland Ser. Appl. Math. Mech., 10, North-Holland, Amsterdam, London, 1970 | MR | Zbl

[16] O. V. Man'ko, V. I. Man'ko, J. Russ. Laser Res., 25:2 (2004), 115–122, arXiv: quant-ph/0401131 | DOI

[17] M. A. Man'ko, J. Russ. Laser Res., 27:5 (2006), 405–413 | DOI

[18] M. A. Man'ko, V. I. Man'ko, R. V. Mendes, J. Russ. Laser Res., 27:6 (2006), 507–532, arXiv: quant-ph/0602189 | DOI

[19] S. N. Filippov, V. I. Man'ko, J. Russ. Laser Res., 31:3 (2010), 211–231, arXiv: 1005.4091 | DOI

[20] G. M. D'Ariano, L. Maccone, M. Paini, J. Opt. B, 5:1 (2003), 77–84, arXiv: quant-ph/0210105 | DOI

[21] S. Weigert, Phys. Rev. Lett., 84:5 (2000), 802–805, arXiv: quant-ph/9903103 | DOI | MR | Zbl

[22] M. A. Man'ko, V. I. Man'ko, Found. Phys., 41:3 (2011), 330–344 | DOI | MR | Zbl

[23] V. I. Man'ko, G. Marmo, E. C. G. Sudarshan, F. Zaccaria, Phys. Lett. A, 327:5–6 (2004), 353–364 | DOI | MR | Zbl

[24] V. I. Man'ko, G. Marmo, A. Simoni, F. Ventriglia, Phys. Lett. A, 372:43 (2004), 6490–6497, arXiv: 0807.0329 | DOI | MR

[25] J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Phys. Rev. Lett., 23:15 (1969), 880–884 | DOI

[26] B. S. Cirel'son, Lett. Math. Phys., 4:2 (1980), 93–100 | DOI | MR