The PPT$$^2$$ Conjecture Holds for All Choi-Type Maps
Satvik Singh, Ion Nechita
Abstract
Abstract We prove that the PPT $$^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow/> <mml:mn>2</mml:mn> </mml:msup> </mml:math> conjecture holds for linear maps between matrix algebras which are covariant under the action of the diagonal unitary group. Many salient examples, like the Choi-type maps, depolarizing maps, dephasing maps, amplitude damping maps, and mixtures thereof, lie in this class. Our proof relies on a generalization of the matrix-theoretic notion of factor width for pairwise completely positive matrices, and a complete characterization in the case of factor width two.
Topics & Concepts
ConjectureMathematicsDiagonalGeneralizationCovariant transformationPure mathematicsType (biology)Class (philosophy)Matrix (chemical analysis)Unitary stateSalientCharacterization (materials science)CombinatoricsDiscrete mathematicsAlgebra over a fieldMathematical analysisGeometryPhysicsComputer scienceLawOpticsEcologyBiologyComposite materialMaterials scienceArtificial intelligencePolitical scienceAdvanced Topics in AlgebraAlgebraic structures and combinatorial modelsMatrix Theory and Algorithms