An effective method of investigation of positive maps on the set of positive definite operators

DOI10.1016/0034-4877(74)90044-5zbMath0348.60108OpenAlexW1989843252MaRDI QIDQ1234542

Andrzej Jamiołkowski

Publication date: 1974

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(74)90044-5

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Algebraic systems of matrices (15A30) Transition functions, generators and resolvents (60J35) Stochastic matrices (15B51)

Related Items (21)

Merging of positive maps: a construction of various classes of positive maps on matrix algebras ⋮ Convolution algebra of superoperators and nonseparability witnesses for quantum operations ⋮ On Functionally Commutative Quantum Systems ⋮ On maps which preserve semipositivity and quantifier elimination theory for real numbers ⋮ Necessary conditions for optimality of decomposable entanglement witnesses ⋮ Global Geometric Difference Between Separable and Positive Partial Transpose States ⋮ Quantifier elimination theory and maps which preserve semipositivity ⋮ Witnessing nonseparability of bipartite quantum operations ⋮ Indecomposable exposed positive bi-linear maps between two by two matrices ⋮ Generalizing Choi-like maps ⋮ A Note on Positive Maps and Classification of States ⋮ FACIAL STRUCTURES FOR VARIOUS NOTIONS OF POSITIVITY AND APPLICATIONS TO THE THEORY OF ENTANGLEMENT ⋮ Some Remarks on the Role of Minimal Length of Positive Maps in Constructing Entanglement Witnesses ⋮ On the Relation between States and Maps in Infinite Dimensions ⋮ Various notions of positivity for bi-linear maps and applications to tri-partite entanglement ⋮ Schrödinger and related equations as Hamiltonian systems, manifolds of second-order tensors and new ideas of nonlinearity in quantum mechanics ⋮ DUALITIES AND POSITIVITY IN THE STUDY OF QUANTUM ENTANGLEMENT ⋮ On semipositive definiteness of \(2n\)-degree forms ⋮ ON APPLICATIONS OF PI-ALGEBRAS IN THE ANALYSIS OF QUANTUM CHANNELS ⋮ The structural physical approximations and optimal entanglement witnesses ⋮ Exposedness of Choi-Type Entanglement Witnesses and Applications to Lengths of Separable States

Cites Work

• Linear transformations which preserve Hermitian and positive semidefinite operators
• Linear transformations which preserve trace and positive semidefiniteness of operators

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