Quantum random walk approximation in Banach algebra

Journal of Mathematical Analysis and Applications

Volumn 430, Issue 1, 2015, Pages 465-482

  Das, B Krishna ^a   Lindsay, J Martin ^b  

^a INDIAN STATISTICAL INSTITUTE   (India)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Matrix space; Noncommutative probability; Quantum random walk; Quantum stochastic cocycle; Quantum Wiener integral; Sesquilinear process

Indexed keywords

EID: 84929505893     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2015.02.039     Document Type: Article

References (21)

1. Attal S., Pautrat Y. From repeated to continuous quantum interaction. Ann. Henri Poincaré 2006, 7(1):59-104.
2. Belton A.C.R. Approximation via toy Fock space - the vacuum-adapted viewpoint. Quantum Stochastics and Information 2008, 3-22. World Scientific, Singapore. V.P. Belavkin, M. Guta (Eds.).
3. Belton A.C.R. Random-walk approximation to vacuum cocycles. J. Lond. Math. Soc. (2) 2010, 81:412-434.
4. A.C.R. Belton, M. Gnacik, J.M. Lindsay, Strong convergence of quantum random walks via semigroup decomposition, preprint (2015).
5. B. Das, J.M. Lindsay, Lévy processes on compact quantum groups and equivariant stochastic flows on noncommutative manifolds, preprint, (2014).
6. Das B.K., Lindsay J.M. Elementary evolutions in Banach algebra. J. Ramanujan Math. Soc. 2013, 28(4):483-497.
7. B.K. Das, J.M. Lindsay, Quantum stochastic analysis in operator space, in preparation.
8. Das B.K., Lindsay J.M., Tripak O. Sesquilinear quantum stochastic analysis in Banach space. J. Math. Anal. Appl. 2014, 409(2):1032-1051.
9. Effros E.G., Ruan Z.-J. Operator Spaces. London Mathematical Society Monographs, New Series 2000, vol. 23. Oxford University Press, Oxford.
10. Evans M.P. Existence of quantum diffusions. Probab. Theory Related Fields 1989, 81(4):473-483.
11. Franz U., Skalski A.G. Approximation of quantum Lévy processes by quantum random walks. Proc. Indian Acad. Sci. Math. Sci. 2008, 118(2):281-288.
12. Hudson R.L., Parthasarathy K.R. Quantum ItÔ's formula and stochastic evolution. Comm. Math. Phys. 1984, 93(3):301-323.
13. Lindsay J.M. Quantum stochastic analysis - an introduction. Lecture Notes in Math. 2005, vol. 1865:181-271. Springer-Verlag, Heidelberg. U. Franz, M. Schürmann (Eds.).
14. Lindsay J.M., Skalski A.G. Quantum stochastic convolution cocycles II. Comm. Math. Phys. 2008, 280(3):575-610.
15. *-algebra. Bull. Lond. Math. Soc. 2001, 33(5):613-621.
16. *-algebra. J. Lond. Math. Soc. 2003, 68(1):255-272.
17. J.M. Lindsay, S.J. Wills, Quantum stochastic cocycles and completely bounded semigroups on operator spaces II, preprint, 2014.
18. Meyer P.-A. Quantum Probability for Probabilists. Lecture Notes in Math. 1995, vol. 1538. Springer-Verlag, Berlin. 2nd edition.
19. Parthasarathy K.R. Introduction to Quantum Stochastic Calculus. Monographs in Mathematics 1992, vol. 85. Birkhäuser, Basel.
20. Sahu L. Quantum random walks and their convergence to Evans-Hudson flows. Proc. Indian Acad. Sci. Math. Sci. 2008, 118(3):443-465.
21. Schürmann M. White Noise on Bialgebras. Lecture Notes in Math. 1993, vol. 1544. Springer, Heidelberg.