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arXiv:quant-ph/0301110

Classical and quantum noise in measurements and transformations

Giacomo Mauro, A. Volta

Published Jan 21, 2003• 3 citations
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Abstract

This paper has been withdrawn. See quant-ph/0408115: G. M. D'Ariano, P. Perinotti and P. Lo Presti, Classical randomness in quantum measurements

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［1］D.P. DiVincenzo, Science 270 (1995) 255. ［2］C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A.Peres, and W.K. Wootters, Phys. Rev. Lett. 70 (1993)1895; G.M. D'Ariano, P.Lo Presti, M.F. Sacchi, Phys.Lett. A272 (2000) 32; S. Albeverio and S.M. Fei, Phys.Lett. A276 (2000) 8; S. Albeverio and S.M. Fei, and W.L.Yang, Commun. Theor. Phys. (Beijing, China) 38 (2002)301; Phys. Rev. A66 (2002) 012301. ［3］C.H. Bennett and S.J. Wiesner, Phys. Rev. Lett. 69(1992) 2881; A. Ekert, Phys. Rev. Lett. 67 (1991) 661; D.Deutsch, A. Ekert, P. Rozsa, C. Macchiavello, S. Popescu,and A. Sanpera, Phys. Rev. Lett. 77 (1996) 2828; C.A.Fuchs, N. Gisin, R.B. Griffiths, C-S. Niu, and A. Peres,Phys. Rev. A56 (1997) 1163. ［4］R.F. Werner, Phys. Rev. A40 (1989) 4277. ［5］G. Alber, T. Beth, M. Horodecki, P. Horodecki, R.Horodecki, M. Rotteler, H. Weinfurter, R.F. Werner, and A. Zeilinger, Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, Springer,New York (2001). ［6］D. Bruss, J.I. Cirac, P. Horodecki, F. Hulpke, B. Kraus,M. Lewenstein, and A. Sanpera, J. Mod. Opt. 49 (2002)1399; D. Bruss, J. Math. Phys. 43 (2002) 4237. ［7］S. Popescu, Phys. Rev. Lett. 72 (1994) 797; S. Popescu,Phys. Rev. Lett. 74 (1995) 2619. ［8］J.S. Bell, Physics (N.Y.) 1 (1964) 195. ［9］A. Peres, Phys. Rev. Lett. 76 (1996) 1413; K. Zyczkowski and P. Horodecki, Phys. Rev. A58 (1998) 883. ［10］M. Horodecki and P. Horodecki, Phys. Rev. A59 (1999)4206. ［11］N.J. Cerf, C. Adami, and R.M. Gingrich, Phys. Rev. A60(1999) 898. ［12］M.A. Nielsen and J. Kempe, Phys. Rev. Lett. 86 (2001)5184. ［13］M. Horodecki, P. Horodecki, and R. Horodecki, Phys.Lett. A223 (1996) 1. ［14］B. Terhal, Phys. Lett. A271 (2000) 319; M. Lewenstein,B. Kraus, J.I. Cirac, and P. Horodecki, Phys. Rev. A62(2000) 052310. ［15］A.C. Doherty, P.A. Parrilo, and F.M. Spedalieri, Phys.Rev. Lett. 88 (2002) 187904. ［16］O. Rudolph, quant-ph/0202121; K. Chen and L.A. Wu,Quant. Inf. Comput. 3 (2003) 193. ［17］K. Chen
We present a thorough classification of the isotropic quantum walks on lattices of dimension d=1,2,3d=1,2,3d=1,2,3 with a coin system of dimension s=2s=2s=2. For d=3d=3d=3 there exist two isotropic walks, namely, the Weyl quantum walks presented in the work of D'Ariano and Perinotti [G. M. D'Ariano and P. Perinotti, Phys. Rev. A 90, 062106 (2014)], resulting in the derivation of the Weyl equation from informational principles. The present analysis, via a crucial use of isotropy, is significantly shorter and avoids a superfluous technical assumption, making the result completely general.