Interpolation by completely positive Mapsy

Linear and Multilinear Algebra

Volumn 59, Issue 10, 2011, Pages 1159-1170

  Li, Chi Kwong ^a   Poon, Yiu Tung ^b  

^a The College of William and Mary   (United States)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

Completely positive map; Dilations; Eigenvalues; Hermitian matrices; Majorization; Quantum operations

Indexed keywords

EID: 80053105525     PISSN: 03081087     EISSN: 15635139     Source Type: Journal    
DOI: 10.1080/03081087.2011.585987     Document Type: Article

References (18)

1. M. Argerami and P. Massey, The local form of doubly stochastic maps and joint majorization in II1 factors, Integral Eqns. Operator Theory 61 (2008), p. 119.
2. M.D. Choi, Completely positive linear maps on complex matrices, Linear Algebra Appl. 10 (1975), pp. 285-290.
3. M.D. Choi and C.K. Li, Numerical ranges and dilations, Linear Multilinear Alg. 47 (2000), pp. 35-48.
4. M.D. Choi and C.K. Li, Constrained unitary dilations and numerical ranges, J. Operator Theory 46 (2001), pp. 435-447.
5. G. Dahl, Matrix majorization, Linear Algebra Appl. 288 (1999), pp. 53-73.
6. S. Formin, W. Fulton, C.K. Li, and Y.T. Poon, Eigenvalues, singular values, and Littlewood-Richardson Coefficients, Am. J. Math. 127 (2005), pp. 101-127.
7. J. Holbrook, Private communication, 2008.
8. A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Am. J. Math 76 (1954), pp. 620-630.
9. K. Kraus, States, Effects, and Operations: Fundamental Notions of Quantum Theory, Lectures in Mathematical Physics at the University of Texas at Austin, Lecture Notes in Physics, Vol. 190, Springer-Verlag, Berlin, Heidelberg, 1983.
10. L. Landau and R. Streater, On Birkhoffs theorem for doubly stochastic completely positive maps of matrix algebras, Linear Algebra Appl. 193 (1993), pp. 107-127.
11. C.K. Li and Y.T. Poon, Principal Submatrices of a Hermitian matrix, Linear Multilinear Alg. 51 (2003), pp. 199-208.
12. A.W. Marshall and I. Olkin, Inequalities: The Theory of Majorizations and its Applications, Academic Press, New York, 1979.
13. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, New York, 2000.
14. V.I. Paulsen, Completely Bounded Maps and Dilations, Pitman Research Notes in Mathematical Series, Wiley, New York, 1986.
15. D. Petz, Quantum Information Theory and Quantum Statistics, Springer-Verlag, Heidelberg, 2008.
16. F.D.M. Peria, P.G. Massey, and L.E. Silvestre, Weak matrix majorization, Linear Algebra Appl. 403 (2005), pp. 343-368.
17. L. Skowronek, E. Størmer, and K. Zyczkowski, Cones of positive maps and their duality relations, J. Math. Phys. 50 (2009), p. 062-106.
18. W.F. Stinespring, Positive functions on C -algebras, Proc. Am. Math. Soc. 6 (1955), pp. 211-216.