A Class of Linear Positive Maps in Matrix Algebras II

We provide a class of linear trace preserving positive maps on matrix algebras which is a generalization of that in [7]. A systematic construction by means of spectra of generators of SU(n) is discussed.

[1]  Hiroyuki Osaka,et al.  A series of absolutely indecomposable positive maps in matrix algebras , 1993 .

[2]  Man-Duen Choi Positive semidefinite biquadratic forms , 1975 .

[3]  A. Jamiołkowski Linear transformations which preserve trace and positive semidefiniteness of operators , 1972 .

[4]  E. Størmer On the Jordan structure of *-algebras , 1965 .

[5]  S. Woronowicz Positive maps of low dimensional matrix algebras , 1976 .

[6]  Seung-Hyeok Kye,et al.  Generalized Choi maps in three-dimensional matrix algebra , 1992 .

[7]  J. Eberly,et al.  N-Level Coherence Vector and Higher Conservation Laws in Quantum Optics and Quantum Mechanics , 1981 .

[8]  L. Jakóbczyk,et al.  Geometry of Bloch vectors in two-qubit system , 2001 .

[9]  A. Guyan Robertson Schwarz inequalities and the decomposition of positive maps on C *-algebras , 1983 .

[10]  Kil-Chan Ha,et al.  Atomic positive linear maps in matrix algebras , 1998 .

[11]  B. Terhal A family of indecomposable positive linear maps based on entangled quantum states , 1998, quant-ph/9810091.

[12]  Erling Størmer Decomposition of positive projections onC*-algebras , 1980 .

[13]  Jun Tomiyama,et al.  Indecomposable Positive Maps in Matrix Algebras , 1988, Canadian Mathematical Bulletin.

[14]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[15]  P. M. Mathews,et al.  STOCHASTIC DYNAMICS OF QUANTUM-MECHANICAL SYSTEMS , 1961 .

[16]  H. Osaka Indecomposable positive maps in low dimensional matrix algebras , 1991 .

[17]  Roman S. Ingarden A Memorial Note on the 10th Anniversary of OSID , 2003, Open Syst. Inf. Dyn..

[18]  E. Sudarshan,et al.  Extreme affine transformations , 1976 .

[19]  Erling Størmer,et al.  Extension of positive maps into B (H) , 1986 .

[20]  W. Keith Nicholson Elementary Linear Algebra , 2001 .

[21]  A. Robertson,et al.  Positive extensions of automorphisms of spin factors , 1983, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[22]  Ryszard Horodecki,et al.  Quantum Information , 2001, Acta Physica Polonica A.

[23]  Kil-Chan Ha A class of atomic positive linear maps in matrix algebras , 2003 .

[24]  Man-Duen Choi Completely positive linear maps on complex matrices , 1975 .

[25]  A. Robertson Positive Projections on C*-Algebras and an Extremal Positive Map , 1985 .

[26]  S. Woronowicz Nonextendible positive maps , 1976 .

[27]  H. Osaka A Class of Extremal Positive Maps in 3×3 Matrix Algebras , 1992 .

[28]  William Arveson,et al.  Subalgebras ofC*-algebras , 1969 .