Entangled Markov chains

Annali di Matematica Pura ed Applicata

Volumn 184, Issue 3, 2005, Pages 327-346

  Accardi, Luigi ^a   Fidaleo, Francesco ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Applications of selfadjoint operator algebras to physics; Non commutative probability and statistics; Quantum information theory; Quantum Markov processes; Quantum random walks

Indexed keywords

EID: 24944563519     PISSN: 03733114     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10231-004-0118-4     Document Type: Article

References (40)

1. Accardi, L.: Non commutative Markov chains. In: Proceedings of Internat. School of Math. Phys., pp. 268-295. Camerino 1974
2. Accardi, L.: Topics in quantum probability. Phys. Rep. 77, 169-192 (1981)
3. Accardi, L.: Some trends and problems in quantum probability. In: Quantum probability and applications to the quantum theory of irreversible processes, ed. by L. Accardi, A. Frigerio, V. Gorini. Lect. Notes Math., vol. 1055, pp. 1-19. Berlin: Springer 1984
4. Accardi, L., Fidaleo, F.: Non homogeneous quantum Markov states and quantum Markov fields. J. Funct. Anal. 200, 324-347 (2003)
5. Accardi, L., Fidaleo, F.: Quantum Markov fields. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6, 123-138 (2003)
6. Accardi, L., Watson, G.S.: Quantum random walks and coherent quantum chains. In: Quantum Probability and Applications IV. Lect. Notes Math., vol. 1396, pp. 73-88. Berlin: Springer 1987
7. Aharonov, D., Ambainis, A., Kempe, J., Vazirani, U.V.: Quantum walks on graphs. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 50-59. New York: ACM Press 2001
8. Ambainis, A., Bach, E., Nayak, A., Vishwanath, A., Watrous, J.: One-dimensional quantum walks. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, pp. 37-49. New York: ACM Press 2001
9. Bach, E., Coppersmith, S., Goldschen, M.P., Joynt, R., Watrous, J.: One-dimensional quantum walks with absorption boundaries, quant-ph/0207008 (2002)
10. d. J. Oper. Theory 43, 97-143 (2000)
11. Brun, T. A., Carteret, H.A.: The quantum to classical transition for random walk, quantph/0208195 (2002)
12. Brun, T.A., Carteret, H.A., Ambainis, A.: Quantum walks driven by many coins. Phys. Rev. A 67 (2003), 052317, 17 pp.
13. Brun, T.A., Carteret, H.A., Ambainis, A.: Quantum random walks with decoherent coins. Phys. Rev. A 67 (2003), 032304, 9 pp.
14. Childs, A.M., Farhi, E., Gutmann, S.: An example of the difference between quantum and classical random walks. Quantum Inf. Process. 1, 35-43 (2002)
15. Choi, M.-D.: Completely positive maps on complex matrices. Linear Algebra Appl. 10, 285-290 (1975)
16. Fagnola F., Bidot R.P.: Irreducible and periodic positive maps. Preprint 2003
17. Fagnola, F., Rebolledo, R.: Lectures in qualitative analysis of quantum Markov semi-groups. In: Quantum Probability and White Noise Analysis, vol XIV, ed. by L. Accardi, F. Fagnola. River Edge: World Scientific 2002
18. Fannes, M., Nachtergaele, B., Slegers, L.: Functions of Markov processes and Markov measures. Rev. Math. Phys. 4, 39-64 (1992)
19. Fannes, M., Nachtergaele, B., Werner, R.F.: Finitely correlated states of quantum spin chains. Commun. Math. Phys. 144, 443-490 (1992)
20. Fannes, M., Nachtergaele, B., Werner, R.F.: Finitely correlated pure states. J. Fund. Anal. 120, 511-534 (1994)
21. Fidaleo, F.: Infinite dimensional entangled Markov chains. Preprint 2004
22. Guikhman, I., Skorokhod, A.: Introduction à la théorie des processus aléatoires. Moscow: MIR 1980
23. Kastler, D.: Equilibrium states of matter and operator algebras. In: Symposia mathematica, vol. XX, pp. 49-107. London: Academic Press 1976
24. Kendon, V., Tregenna, B.: Decoherence is useful in quantum walks. quant-ph/0209005 (2002)
25. Kendon, V., Tregenna, B.: Decoherence in a quantum walk on the line. quant-ph/0210047 (2002b)
26. Konno, N.: Quantum random walks in one dimension. Quantum Inf. Process. 1, 345-354 (2003)
27. Konno, N.: A new type of limit theorems for the one-dimensional quantum random walk, quant-ph/0206103 (2002)
28. Konno, N.: Limit theorems and absorpion problems for quantum random walks in one dimension. Quantum Inf. Comput. 2, Suppl., 578-595 (2002)
29. Konno, N., Namiki, T., Soshi, T.: Symmetry of distribution for the one-dimensional Hadamard walk. Interdiscip. Inf. Sci. 10, 11-22 (2004)
30. Konno, N., Namiki, T., Soshi, T., Sudbury, A.: Absorption problems for quantum random walks in one dimension. J. Phys. A 36, 241-253 (2003)
31. 1. quant-ph/0209100 (2002)
32. Mackay, T.D., Bartlett, S.D., Stephanson, L.T., Sanders, B.C.: Quantum walks in higher dimensions. J. Phys. A 35, 2747-2753 (2002)
33. Meyer, D.A.: From quantum cellular automata to quantum lattice gases. J. Stat. Phys. 85, 551-574 (1996)
34. Moore, C., Russell, A.: Quantum walks on the hypercubes. quant-ph/0104137 (2001)
35. Nachtergaele, B.: The spectral gap for some spin chains with discrete symmetry breaking. Commun. Math. Phys. 175, 565-606 (1992)
36. Nachtergaele, B.: Quantum Markov chains: applications to physics. Centra V. Volterra, preprint n. 497 (2001)
37. Schaefer, H.H.: Banach Lattices and positive operators. Berlin, Heidelberg, New York: Springer 1974
38. Severini, S.: Line diagrams and line quantumrandom walks. Preprintquant-ph/0210055 (2002)
39. Travaglione, B.C., Milburn, G.J.: Implementing the quantum random walk. Phys. Rev. A 65 (2002), 032310, 5 pp.
40. Yamasaki, T., Kobayashi, H., Imai, H.: An analysis of absorbing times of quantum walks. Lect. Notes Comput. Sci., vol. 2509, pp. 315-329. Berlin: Springer 2002