When do pieces determine the whole? Extreme marginals of a completely positive map

DOI10.1142/S0129055X14500020zbMath1287.81014arXiv1209.5933OpenAlexW3098910111WikidataQ62561381 ScholiaQ62561381MaRDI QIDQ5411793

Erkka Haapasalo, Teiko Heinosaari, Juha-Pekka Pellonpää

Publication date: 25 April 2014

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

Full work available at URL: https://arxiv.org/abs/1209.5933

zbMATH Keywords

completely positive mapquantum channelquantum instrumentconvex extreme point

Mathematics Subject Classification ID

Applications of operator algebras to the sciences (47L90) Quantum measurement theory, state operations, state preparations (81P15) Vector-valued measures and integration (46G10) Positive linear operators and order-bounded operators (47B65) Operator algebra methods applied to problems in quantum theory (81R15) Tensor products of linear operators (47A80)

Related Items (9)

Diagonal couplings of quantum Markov chains ⋮ Barycentric decomposition for quantum instruments ⋮ Optimal quantum observables ⋮ Covariant KSGNS construction and quantum instruments ⋮ Uniqueness of the joint measurement and the structure of the set of compatible quantum measurements ⋮ Reduction and extremality of finite observables ⋮ Witnessing incompatibility of quantum channels ⋮ Post-processing minimal joint observables ⋮ Compatibility properties of extreme quantum observables

Cites Work

• Unnamed Item
• Notes on joint measurability of quantum observables
• Completely positive linear maps on complex matrices
• Subalgebras of \(C^ *\)-algebras
• Complete characterization of extreme quantum observables in infinite dimensions
• Radon–Nikodym derivatives of quantum operations
• Completely positive module maps and completely positive extreme maps
• Quantum instruments: I. Extreme instruments
• Classical randomness in quantum measurements

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