"My bound" has appeared in the article

B.S. Cirel'son, "Quantum generalizations of Bell's inequality." Lett. Math. Phys. 4:2, 93-100 (1980). [MR81e:81011] [download]

See also:

A. Chefles, S.M. Barnett, "Complementarity and Cirel'son's inequality." J. Phys. A 29:10, L237-L239 (1996). [MR97b:81002]

A. Peres, "Quantum theory." Kluwer Academic, 1993.

The stunning implications of Bell's theorem caused an outbreak of theoretical activity, including some wild speculations that I shall not discuss. On the serious side, Bell's work led to a systematic search for other inequalities with the same universal character.

Cirel'son's inequality

Cirel'son raised the question whether quantum theory imposed an upper limit to correlations between distant events (a limit which would of course be higher than the classical one, given by Bell's inequality).
(Peres, Sect. 6-5 on p. 185.)

Though, I just answered the question. It was A. Vershik who raised it. Sorry, I did not mention him in 1980; but I did so in 1992, see Found. Phys. 22:7, p. 884.

First result: citing works (1980-2010)

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  0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0
1980                1990                2000                2010

Acin, Ahanj, Ahn, Anders, Andersson, Aravind, Aspect, Augusiak, Banaszek, Barnett, Barnum, Barrett, Bechmann-Pasquinucci, Beigi, Belinskii, Bergou, Berry, Boixo, Bouwmeester, Bovino, Braunstein, Brassard, Broadbent, Browne, Brukner, Brunner, Bruss, Bub, Buhrman, Busshardt, Butterfield, Cabello, Castagnoli, Castelletto, Cereceda, Cerf, Chefles, Chen, Christandl, Choudhary, Chuang, Clark, Collins, Craig, D'Ariano, De Baere, De Martini, De Neve, Degiovanni, De Raedt, Dieks, Doherty, Dotsenko, Dowker, Durt, Eberhard, Elliott, Freyberger, Gazi, Ghosh, Gisin, Gnacinski, Gour, Grangier, Grib, Grosshans, Hafezi, Haug, Henson, Hillery, Horne, Horodecki, Hou, Howell, Ichikawa, Invernizzi, Ito, Jabs, Jeong, Joag, Johansen, Kar, Kaszlikowski, Keimpema, Kempe, Keyl, Khanna, Kim, Klyshko, Kobayashi, Kunkri, Kwek, Lamas-Linares, Landau, Larsson, Laskowski, Latorre, Lee, Leifer, Liang, Linden, Locajicek, Loock, Loubenets, Lupo, Major, Mann, Man'ko, Marmo, Marcovitch, Masanes, Mataloni, Matsui, Mello, Methot, Michielsen, Miklaszewski, Miyashita, Nakamura, Neumaier, Nielsen, Oh, Olivares, Pan, Paris, Paterek, Paternostro, Pati, Peres, Piani, Pitowsky, Polubarinov, Popescu, Portmann, Preda, Rahaman, Rai, Ralph, Redei, Regev, Resch, Revzen, Reznik, Rideout, Roberts, Rohrlich, Rossi, Roy, Ryu, Santana, Scarani, Schlingemann, Seevinck, Shimony, Short, Skrzypczyk, Son, Sorkin, Spekkens, Stairs, Stepanik, Summers, Sun, Svozil, Stobinska, Tapp, Toner, Tsutsui, Tualle-Brouri, Uffink, Unger, Vaidman, Vallone, Verch, Vinduska, Voronov, Walther, Wehner, Wenger, Werner, Wilce, Wilke, Wilson, Winter, Wodkiewicz, Wolf, Wuthrich, Yang, Yao, Yu, Zeilinger, Zhang, Zhao, Zukowski. (Detail)

My subsequent articles on quantum Bell-type inequalities culminate in the survey

B.S. Tsirelson, "Some results and problems on quantum Bell-type inequalities." Hadronic Journal Supplement 8:4, 329-345 (1993). [download]

Subsequent results: citing works (1985-2010)

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  *********************** 7 8 9 0 1 2 3 4 5 6 7 8 9 0
1985      1990                2000                2010

Acin, Ajoy, Allcock, Ann, Auletta, Avis, Avron, Bacon, Badziag, Barnett, Barrett, Basoalto, Bell, Branciard, Brennen, Brunner, Buhrman, Cabello, Cerf, Christandl, Cleve, Cohen, Colbeck, Dahlsten, Degorre, Doherty, Dowker, Filipp, Fishburn, Fitzi, Forster, Fritz, Genovese, Gisin, Greenberger, Gross, Hanggi, Heydari, Hillery, Hoyer, Hsu, Iblisdir, Imai, Ito, Jaeger, Jones, Junge, Kaszlikowski, Kenneth, Khalfin, Krenn, Laplante, Leifer, Linden, Luo, Masanes, Massar, Methot, Moriyama, Morgan, Muller, Navascues, Owari, Pachos, Pal, Palazuelos, Paterek, Pawlowski, Percival, Perez-Garcia, Pino, Pironio, Pitowski, Popescu, Reeds, Regev, Rideout, Roberts, Rohrlich, Roland, Rungta, Scarani, Scholz, Skrzypczyk, Slingerland, Slofstra, Summers, Svozil, Toner, Unger, Upadhyay, Vaidman, Verstraete, Vertesi, Villanueva, Watrous, Wehner, Werner, Wiesniak, Winkler, Winter, Wolf, Wu, Yurke, Zukowski. (Detail)