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Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state.
Linear transformations which preserve trace and positive semidefiniteness of operators
A. Jamiołkowski · 1972
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Finite Dimensional Multilinear Algebra. Part I
M. Marcus · 1973
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Completely positive linear maps on complex matrices
M.-D. Choi · 1975
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The ’transition probability’ in the state space of a ∗ –algebra
A. Uhlmann · 1976
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Some variations on the numerical range
M. Marcus and B. Wang · 1980
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Matrix Analysis
A. Horn and C. R. Johnson · 1985
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Restricted numerical range and weak convergence on the boundary of the numerical range
K. Das, S. Mazumdar, and B. Sims · 1987
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The numerical range and decomposable numerical range of matrices
N. Bebiano, C. K. Li, and J. da Providencia · 1991
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Topics in Matrix Analysis
A. Horn and C. R. Johnson · 1994
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Special Issue: The Numerical Range and Numerical Radius
T. Ando and C. K. Li · 1994
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C-numerical ranges and C-numerical radii
C. K. Li · 1994
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Fidelity for Mixed Quantum States
R. Jozsa · 1994
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Separability of mixed states: necessary and sufficient conditions
M. Horodecki, P. Horodecki, and R. Horodecki · 1996
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Mixed-state entanglement and quantum error correction
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters · 1996
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Numerical Range: The Field of Values of Linear Operators and Matrices
K. E. Gustafson and D. K. M. Rao · 1997
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Theory of quantum error-correcting codes
E. Knill and R. Laflamme · 1997
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Local description of quantum inseparability
A. Sanpera, R. Tarrach, and G. Vidal · 1998
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A Schmidt number for density matrices
B. Terhal and P. Horodecki · 2000
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Evidence for bound entangled states with negative partial transpose
D.P. DiVincenzo, P.W. Shor, J.A. Smolin, B.M. Terhal, and A.V. Thapliyal · 2000
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Local distinguishability of multipartite orthogonal quantum states
J. Walgate, A. J. Short, L. Hardy, and V. Vedral · 2000
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Induced operators on symmetry classes of tensors
C. K. Li and A. Zaharia · 2001
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A new concept for block operator matrices: the quadratic numerical range
H. Langer, A. Markus, A. Matsaev, and C. Tretter · 2001
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Minkowski geometric algebra of complex sets
R. T. Farouki, H. P. Moon, and B. Ravani · 2001
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Optimal creation of entanglement using a two-qubit gate
B. Kraus and J. I. Cirac · 2001
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Minimal entropy of states emerging from noisy quantum channels
C. King and M. B. Ruskai · 2001
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Exact Minkowski products of n n complex discs
R. T. Farouki and H. Pottmann · 2002
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The Significance of the c c -Numerical Range and the Local c -Numerical Range in Quantum Control and Quantum Information
T. Schulte-Herbrüggen, G. Dirr, Helmke U., and S. J. Glaser · 2008
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On the dimension of subspaces with bounded Schmidt rank
T. Cubitt, A. Montanaro, and A. Winter · 2008
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Spectral properties of entanglement witnesses
G. Sarbicki · 2008
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Quantum Information Theory and Quantum Statistics
D. Petz · 2008
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Quantum state discrimination: a geometric approach
D. Markham, J. A. Miszczak, Z. Puchała, and K. Życzkowski · 2008
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Research problems on numerical ranges in quantum computing
D. W. Kribs, A. Pasieka, M. Laforest, C. Ryan, and M. P. Silva · 2009
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Additivity for unital qubit channels
C. King · 2002
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Concurrence in arbitrary dimensions
P. Badzia̧g, P. Deuar, M. Horodecki, P. Horodecki, and R. Horodecki · 2002
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Geometric measure of entanglement for multipartite quantum states
T.-C. Wei and P. M. Goldbart · 2003
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Statistical properties of random density matrices
H.-J. Sommers and K. Życzkowski · 2004
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Wehrl entropy, Lieb conjecture, and entanglement monotones
F. Mintert and K. Życzkowski · 2004
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A quantum computing primer for operator theorists
D. W. Kribs · 2005
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Real numerical range
J. Holbrook · 2009
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Numerical ranges and minimal fidelity guarantees
N. R. Silva · 2009
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A Family of Norms With Applications In Quantum Information Theory, 2009
N. Johnston and D. Kribs · 2009
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Positive maps, positive polynomials and entanglement witnesses
Ł. Skowronek and K. Życzkowski · 2009
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Cones of positive maps and their duality relations
Ł. Skowronek, E. Størmer, and K. Życzkowski · 2009
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Necessary and sufficient conditions for bipartite entanglement
J. Sperling and W. Vogel · 2009
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A counterexample to additivity of minimum output entropy
M. B. Hastings · 2009
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The geometric measure of entanglement for a symmetric pure state with positive amplitudes
M. Hayashi, D. Markham, M. Murao, M. Owari, and S. Virmani · 2009
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The geometric measure of entanglement for symmetric states
R. Hübener, M. Kleinmann, T.-C. Wei, and O. Gühne · 2009
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Gradient Flows for Optimisation and Quantum Control: Foundations and Applications, 2010
T. Schulte-Herbrüggen, S. J. Glaser, G. Dirr, and U. Helmke · 2010
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Product numerical range in a space with a tensor product structure
Z. Puchała, P. Gawron, J.A. Miszczak, Ł. Skowronek, Choi M.-D., and K. Życzkowski · 2010
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A few steps more towards NPT bound entanglement
Ł. Pankowski, M. Piani, M. Horodecki, and P. Horodecki · 2010
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Protected Subspaces in Quantum Information
K. Majgier, H. Maassen, and K. Życzkowski · 2010
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