An analysis of completely positive trace-preserving maps on M2

Linear Algebra and Its Applications

Volumn 347, Issue 1-3, 2002, Pages 159-187

  Ruskai, Mary Beth ^a   Szarek, Stanislaw ^b,c   Werner, Elisabeth ^b,d  

^a UNIVERSITY OF MASSACHUSETTS LOWELL   (United States)

^b CASE WESTERN RESERVE UNIVERSITY   (United States)

^c SORBONNE UNIVERSITÉ   (France)

^d UNIV LILLE   (France)

Author keywords

Bloch sphere; Completely positive maps; Noisy channels; Quantum communication; States; Stochastic maps

Indexed keywords

QUANTUM COMMUNICATION; QUANTUM THEORY;

BLOCH SPHERE; COMPLETELY POSITIVE MAP; NOISY CHANNEL; STATES; STOCHASTIC MAPS;

STOCHASTIC SYSTEMS;

EID: 31244433606     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0024-3795(01)00547-x     Document Type: Article

References (26)

1. A. Fujiwara, P. Algoet, Affine parameterization of completely positive maps on a matrix algebra, preprint;
2. A. Fujiwara, P. Algoet, One-to-one parameterization of quantum channels, Phys. Rev. A 59 (1999) 3290-3294.
3. G.G. Amosov, A.S. Holevo, R.F. Werner, On some additivity problems in quantum information theory (lanl:quant-ph/0003002, preprint).
4. C.H. Bennett, P.W. Shor, Quantum information theory, IEEE Trans. Inform. Theory (1998).
5. M.-D. Choi, Completely positive linear maps on complex matrices, Linear Algebra Appl. 10 (1975) 285-290.
6. C. Fuchs, Nonorthogonal quantum states maximize classical information capacity, Phys. Rev. Lett. 79 (1997) 1162-1165 (lanl: quant-ph/9703043, preprint).
7. R. Haag, D. Kastler An algebraic approach to quantum field theory, J. Math. Phys. 5 (1964) 848-861.
8. A.S. Holevo, On the capacity of quantum communication channel, Probl. Peredachi Inform. 15 (4) (1979) 3-11
9. ([English Trans.; Problems of Information Transm. 15 (4) (1979) 247-253]).
10. A.S. Holevo, Quantum coding theorems, Russian Math. Surveys 53 (6) (1999) 1295-1331 (quant-ph/9809023).
11. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
12. M. Horodecki, P. Horodecki, Reduction criterion of separability and limits for a class of protocols of entanglement distillation. Available from: xxx.lanl.gov (quant-ph/9708015, preprint).
13. C. King, M.B. Ruskai, Minimal entropy of states emerging from noisy quantum channels, IEEE Trans. Inform. Theory 47 (2001) 192-209.
14. C. King, M.B. Ruskai, Capacity of quantum channels using product measurements, J. Math. Phys. 42 (2001) 87-98.
15. K. Kraus, General state changes in quantum theory, Ann. Physics 64 (1971) 311-335
16. K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory, Springer, Berlin, 1983.
17. G. Lindblad, Completely positive maps and entropy inequalities, Commun. Math. Phys. 40 (1975) 147-151.
18. S. Lloyd, Science 273 (1996) 1073.
19. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, Cambridge, 2000.
20. Niu, Griffiths, Two qubit copying machine for economical quantum eavesdropping, quantph/9810008.
21. V.I. Paulsen, Completely Bounded Maps and Dilations, Pitman Research Notes in Mathematics Series, vol. 146, Longman, Harlow, Wiley, New York, 1986.
22. G. Pedersen, C *-Algebras and Their Automorphism Groups, Academic Press, New York, 1979.
23. E. Rieffel, C. Zalka, private communications and unpublished manuscript.
24. B.M. Terhal, I.L. Chuang, D.P. DiVincenzo, M. Grassl, J.A. Smolin, Simulating quantum operations with mixed environments (quant-ph/9806095).
25. B. Schumacher, M.D. Westmoreland, Optimal signal ensembles. Available form: xxx.lanl.gov (quant-ph/9912122, preprint).
26. M.B. Ruskai, S. Szarek, E. Werner. Available form: xxx.lanl.gov (quant-ph/0005004, preprint).