Quantum channels, wavelets, dilations and representations of On

Proceedings of the Edinburgh Mathematical Society

Volumn 46, Issue 2, 2003, Pages 421-433

  Kribs, David W ^a,b  

^a UNIVERSITY OF GUELPH   (Canada)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Completely positive map; Cuntz algebra; Isometric dilation; Operator; Orthogonal wavelet; Quantum channel

Indexed keywords

EID: 0042414129     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0013091501000980     Document Type: Conference Paper

References (22)

1. G. AMOSOV, A. HOLEVO AND R. F. WERNER, On some additivity problems in quantum information theory. Probl. Inform. Transmission 36 (2000), 25-34.
2. W. ARVESON, Subalgebras of C*-algebras. II, Acta Math. 128 (1972), 271-308.
3. O. BRATTELI AND P. JORGENSEN, Wavelet filters and infinite-dimensional unitary groups, in Wavelet Analysis and Applications, Guangzhou, 1999, pp. 35-65; American Mathematical Society/International Press Studies in Advanced Mathematics, vol. 25 (American Mathematical Society, Providence, RI, 2002).
4. O. BRATTELI, D. EVANS AND P. JORGENSEN, Compactly supported wavelets and representations of the Cuntz relations, Appl. Computat. Harmon. Analysis 8 (2000), 166-196.
5. d, J. Operat. Theory 43 (2000), 97-143.
6. J. BUNCE, Models for n-tuples of non-commuting operators, J. Funct. Analysis 57 (1984), 21-30.
7. M. D. CHOI. Completely positive linear maps on complex matrices, Linear Algebra Applic. 10 (1975), 285-290.
8. I. CHUANG AND M. NIELSEN, Quantum computation and quantum information (Cambridge University Press, 2000).
9. K. DAVIDSON AND D. PITTS, Invariant subspaces and hyper-reflexivity for free semi-group algebras, Proc. Land. Math. Soc. 78 (1999), 401-430.
10. K. DAVIDSON, E. KATSOULIS AND D. PITTS, The structure of free semigroup algebras, J. Reine Angew. Math. 533 (2001), 99-125.
11. K. DAVIDSON, D. KRIBS AND M. SHPIGEL, Isometric dilations of non-commuting finite rank n-tuples, Can. J. Math. 53 (2001), 506-545.
12. A. FRAZHO, Models for non-commuting operators, J. Funct. Analysis 48 (1982), 1-11.
13. J. GLIMM, Type I C*-algebras, Math. Ann. 73 (1961), 572-612.
14. J. HOLBROOK, D. KRIBS AND R. LAFLAMME, Generalized quantum error correction and the structure of the commutant, in preparation (2003).
15. P. JORGENSEN, Minimality of the data in wavelet filters, Adv. Math. 159 (2001), 143-228.
16. P. JORGENSEN AND D. KRIBS, Wavelet representations and Fock space on positive matrices, J. Funct. Analysis 197 (2003), 526-559.
17. C. KING, Additivity for a class of unital qubit channels, J. Math. Phys. 43 (2002), 4641-4653.
18. K. KRAUS, General state changes in quantum theory, Ann. Phys. 64 (1971), 311-335.
19. V. PAULSEN, Completely bounded maps and dilations, Pitman Research Notes in Mathematics, vol. 146 (Longman Science Technology. Harlow, 1986).
20. G. POPESCU, Isometric dilations for infinite sequences of noncommuting operators, Trans. Am. Math. Soc. 316 (1989), 523-536.
21. 2, Linear Algebra Applic. 347 (2002), 159-187.
22. P. SHOR, Additivity of the classical capacity of entanglement-breaking quantum channels, Quantum information theory, J. Math. Phys. 43 (2002), 4334-4340.