Radon–Nikodym derivatives of quantum instruments

DOI10.1063/1.532385zbMath1056.81502OpenAlexW2089281278MaRDI QIDQ4661539

Alexandr S. Holevo

Publication date: 30 March 2005

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

Full work available at URL: https://doi.org/10.1063/1.532385

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Applications of selfadjoint operator algebras to physics (46L60) Quantum measurement theory, state operations, state preparations (81P15)

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Radon–Nikodym derivatives of quantum operations ⋮ Electromagnetism in terms of quantum measurements ⋮ Kolmogorov decompositions and extremality conditions for positive covariant kernels ⋮ Why unsharp observables? ⋮ Covariant KSGNS construction and quantum instruments ⋮ Covariant CP-instruments and their convolution semigroups ⋮ The structure of invariant α-CP multilinear maps and associatedJ-representations ⋮ Complete measurements of quantum observables ⋮ Entanglement-breaking channels in infinite dimensions ⋮ Modules and extremal completely positive maps ⋮ Realization schemes for quantum instruments in finite dimensions ⋮ Covariant quantum instruments ⋮ Barycentric decomposition of quantum measurements in finite dimensions ⋮ Radon–Nikodým type theorem for α-completely positive maps ⋮ On the counting of quantum errors ⋮ Decomposition of time-covariant operations on quantum systems with continuous and∕or discrete energy spectrum ⋮ Entropy reduction of quantum measurements ⋮ Optimal covariant quantum measurements

Cites Work

• An operational approach to quantum probability
• Quantum stochastic calculus, operation valued stochastic processes, and continual measurements in quantum mechanics
• Quantum counting processes
• Canonical approximate quantum measurements
• An Algebraic Approach to Quantum Field Theory