Biased Random Number Generator Based on Bell's Theorem
Yong-Gang Tan** , Yao-Hua Hu, Hai-Feng Yang
Physics and Information Engineering Department, Luoyang Normal College, Luoyang 471022
Abstract ：We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser–Horne inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of 0s to 1s varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.
收稿日期: 2015-10-27
出版日期: 2016-03-31
:
03.65.Ud
(Entanglement and quantum nonlocality)
03.67.Mn
(Entanglement measures, witnesses, and other characterizations)
[1] Bennett C H and Brassard G 1984 Proceeding IEEE International Conference of Computers, Systems, and Signal Processing (New York: IEEE) p 175 [2] Ekert A K 1991 Phys. Rev. Lett. 67 661 [3] Gisin N, Ribordy G, Tittel W and Zbinden H 2002 Rev. Mod. Phys. 74 145 [4] Rarity J G, Owens P C M and Tapster P R 1994 J. Mod. Opt. 41 2435 [5] Jennewein T, Achleitner U, Weihs G, Weinfurter H and Zeilinger A 2000 Rev. Sci. Instrum. 71 1675 [6] Gabriel C, Wittmann C and Sych D 2010 Nat. Photon. 4 711 [7] Jian Y, Ren M, Wu E, Wu G and Zeng H 2011 Rev. Sci. Instrum. 82 073109 [8] Ren M, Wu E, Liang Y, Jian Y, Wu G and Zeng H 2011 Phys. Rev. A 83 023820 [9] Sanguinetti B, Martin A, Zbinden H and Gisin N 2014 Phys. Rev. X 4 031056 [10] Marandi A, Leindecker N C, Vodopyanov K L and Byer R L 2012 Opt. Express 20 19322 [11] England D G, Bustard P J, Moffatt D J, Nunn J and Lausten R 2014 Appl. Phys. Lett. 104 051117 [12] Pironio S, Acín A, Massar S, Boyer D L G A and Matsukevich D N 2010 Nature 464 1021 [13] Bell J S 1965 Phsycis 1 195 [14] Clauser J F, Horne M A, Shimony A and Holt R A 1969 Phys. Rev. Lett. 23 880 [15] Clauser J and Horne M A 1974 Phys. Rev. D 10 526 [16] Freedman S and Clauser J 1972 Phys. Rev. Lett. 28 938 [17] Aspect A, Grangier P and Roger G 1981 Phys. Rev. Lett. 47 460 [18] Aspect A, Dalibard J and Roger G 1982 Phys. Rev. Lett. 49 1804 [19] Aspect A, Grangier P and Roger G 1982 Phys. Rev. Lett. 49 91 [20] Ou Z and Mandel L 1988 Phys. Rev. Lett. 61 50 [21] Shih Y and Alley C 1988 Phys. Rev. Lett. 61 2921 [22] Kwiat P et al 1995 Phys. Rev. Lett. 75 4337 [23] Weihs G, Jennewein T, Simon C, Weinfurter H and Zeilinger A 1998 Phys. Rev. Lett. 81 5039 [24] Tittel W, Brendel J, Zbinden H and Gisin N 1998 Phys. Rev. Lett. 81 3563 [25] Rowe M A, Kielpinski D, Meyer V et al 2001 Nature 409 791 [26] Ansmann M, Wang H, Bialczak R C, Hofheinz M, Lucero E, Neeley M, O'Connell A D, Sank D, Weides M, Wenner J, Cleland A N and Martinis J M 2009 Nature 461 504 [27] Hofmann J, Krug M, Ortegel N, Gérard L, Weber M, Rosenfeld W and Weinfurter H 2012 Science 337 72 [28] Scheidl T, Ursin R, Kofler J et al 2010 Proc. Natl. Acad. Sci. USA 107 19708 [29] Acín A, Brunner N, Gisin N et al 2007 Phys. Rev. Lett. 98 230501 [30] Pironio S, Acín A, Brunner N et al 2009 New J. Phys. 11 045021 [31] Masanes L, Pironio S and Acin A 2011 Nat. Commun. 2 238 [32] H?nggi E and Renner R 2010 arXiv:1009.1833v2 [quant-ph] [33] Li H W, Paw?owski M, Yin Z Q, Guo G C and Han Z F 2012 Phys. Rev. A 85 052308 [34] Lo H K, Chau H F and Ardehali M 2005 J. Cryptology 18 133 [35] Eberhard P H 1993 Phys. Rev. A 47 R747 [36] Brunner N, Gisin N, Scarani V and Simon C 2007 Phys. Rev. Lett. 98 220403 [37] Cabello A and Larsson J A 2007 Phys. Rev. Lett. 98 220402 [38] Tamaki K, Koashi M and Imoto N 2003 Phys. Rev. Lett. 90 167904 [39] Tamaki K and Lükenhaus N 2004 Phys. Rev. A 69 032316 [40] Tsirelson B S 1980 Lett. Math. Phys. 4 93 [41] Lucamarini M et al 2012 Phys. Rev. A 86 032325 [42] Ivanovic I D 1987 Phys. Lett. A 123 257 [43] Dieks D 1988 Phys. Lett. A 126 303 [44] Peres A 1988 Phys. Lett. A 128 19 [45] Chelfes A 1988 Phys. Lett. A 128 19 [46] Peres A and Wootters W K 1991 Phys. Rev. Lett. 66 1119
[1]
.
[2]
.
[3]
.
[4]
.
[5]
.
[6]
.
[7]
.
[8]
.
[9]
.
[10]
.
[11]
.
[12]
.
[13]
.
[14]
.
[15]
.
2016, Vol. 33 
