Positive linear maps of operator algebras

By E. Størmer. 2012

541 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/bcb37c17db62c4e6a3d6231efe12bce94c7d57c4

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In Algebra and Number Theory

In Computational Theory and Mathematics

Citations in the corpus

The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement (2012, result): “Using old results of Stormer [134] and of Woronowicz [148], it was shown by Horodecki et al.”
Dynamics of initially entangled open quantum systems (2004, background): “Since positive maps transform such a set into itself, they themselves form a convex compact set [14] (the set of completely positive maps also form a convex set lying inside the convex set of positive maps(3)).”
Fundamentals of quantum information theory (2002, result): “Due to results of StHrmer [148] and Woronowicz”
Tensor Products of C*-Algebras and Operator Spaces (2020, methodology): “It was preceded by important work on positive maps by Kadison and Størmer; see [236] for references and information on the latter maps.”
Geometry of Quantum States: Index (2007, background): “The not completely positive transposition map T allows one to introduce the following definition [861, 217, 219]:”
Noncommutative extensions of classical and multiple recurrence theorems (2003, unknown): “If Φ is positive and x ∈ A is arbitrary then, summing up Kadison’s inequality for a = x + x∗ and for a = i(x − x∗), we have the following inequality of Störmer: Φ(x)∗Φ(x) + Φ(x)Φ(x)∗ 6 ‖Φ‖Φ(x∗x+ xx∗) (see [33]).”
The Theory of Quantum Information (2018, methodology): “10) proved shortly after, it follows that the partial transpose test correctly identifies all entangled state in a tensor product of two complex Euclidean spaces, both of dimension 2 or one of dimension 2 and one of dimension 3, based on work of Størmer [198] and Woronowicz [232], but that entangled”