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The set of doubly-stochastic quantum channels and its subset of mixtures of unitaries are investigated.
Three observations on linear algebra
G. Birkhoff · 1946
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Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiolkowski · 1972
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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Bistochastic operators on finite-dimensional von-Neumann algebras
S.L. Tregub · 1986
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The essentially commutative dilations of dynamical semigroups on M n M_{n}
B. Kümmerer and H. Maassen · 1987
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Angelika Bunse-Gerstner, Ralph Byers, and Volker Mehrmann · 1989
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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 1990
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On Birkhoff’s theorem for doubly stochastic completely positive maps of matrix algebras
L. J. Landau and R. F. Streater · 1993
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Applied Functional Analysis. Main Principles and Their Applications
Eberhard Zeidler · 1995
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Entanglement of assistance
D. P. DiVincenzo, C. A. Fuchs, H. Mabuchi, J. A. Smolin, A. V. Thapliyal, and A. Uhlmann · 1999
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Entanglement measures under symmetry
K.G. H. Vollbrecht and R. F. Werner · 2001
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A. Arias, A. Gheondea, and S. Gudder · 2002
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C. King · 2002
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Computable measure of entanglement
G. Vidal and R.F. Werner · 2002
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Counterexample to an additivity conjecture for output purity of quantum channels
R.F. Werner and A.S. holevo · 2002
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Quantum lost and found
Extremal quantum states in coupled systems
K.R. Parthasarath · 2005
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Contractivity of positive and trace-preserving maps under L p L_{p} norms
D. Pérez-García, M. M. Wolf, D. Petz, and M.B. Ruskai · 2006
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On the minimal number of unitaries needed to describe a random-unitary channel
F. Buscemi · 2006
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Some observations on the Youla form and conjugate-normal matrices
H. Faßbender and Kh. D. Ikramov · 2006
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Simplification of additivity conjecture in quantum information theory
M. Fukuda · 2007
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Simplifying additivity problems using direct sum constructions
M. Fukuda and M. M. Wolf · 2007
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M. Gregoratti and R. F. Werner · 2003
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On extremal quantum states of composite systems with fixed marginals
O. Rudolph · 2004
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Entanglement of assistance and multipartite state distillation
J.A. Smolin, F. Verstraete, and A. Winter · 2005
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http://www.imaph.tu-bs.de/qi/problems/
Open problems in QIT
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Additivity and distinguishability of random unitary channels
B. Rosgen · 2008
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On random unitary channels
Koenraad M. R. Audenaert and Stefan Scheel · 2008
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