Geometry of sets of quantum maps: A generic positive map acting on a high-dimensional system is not completely positive

DOI10.1063/1.2841325zbMath1153.81441arXiv0710.1571OpenAlexW2126946323WikidataQ112267050 ScholiaQ112267050MaRDI QIDQ3544653

Karol Życzkowski, Elisabeth M. Werner, Stanislaw J. Szarek

Publication date: 8 December 2008

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.1571

Mathematics Subject Classification ID

Quantum computation (81P68) Applications of operator theory in the physical sciences (47N50) Quantum measurement theory, state operations, state preparations (81P15) Special matrices (15B99)

Related Items

Separability criterion for quantum effects, Rogers-Shephard inequality for log-concave functions, THE ABSOLUTE POSITIVE PARTIAL TRANSPOSE PROPERTY FOR RANDOM INDUCED STATES, Almost all quantum channels are equidistant, New examples of extremal positive linear maps, Convex set of quantum states with positive partial transpose analysed by hit and run algorithm, Pauli semigroups and unistochastic quantum channels, Dvoretzky's theorem and the complexity of entanglement detection, The inverse eigenvalue problem for entanglement witnesses, Entanglement Thresholds for Random Induced States, Cones of positive maps and their duality relations, Generating random quantum channels, Approximating the set of separable states using the positive partial transpose test, Log-convex set of Lindblad semigroups acting on N-level system

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