Normal Completely Positive Maps on the Space of Quantum Operations

DOI10.1142/S1230161213500030zbMath1275.81010arXiv1012.3197OpenAlexW3101924386WikidataQ62040185 ScholiaQ62040185MaRDI QIDQ4921464

Veronica Umanità, Alessandro Toigo, Giulio Chiribella

Publication date: 10 May 2013

Published in: Open Systems & Information Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3197

zbMATH Keywords

completely positive mapsquantum operationscompletely bounded mapsnoncommutative Radon-Nikodym theoremquantum superinstrumentsquantum supermaps

Mathematics Subject Classification ID

Operator spaces and completely bounded maps (46L07) Quantum measurement theory, state operations, state preparations (81P15) Vector-valued measures and integration (46G10) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Channel models (including quantum) in information and communication theory (94A40)

Related Items (2)

Quantum and classical dynamical semigroups of superchannels and semicausal channels ⋮ Semantics for a quantum programming language by operator algebras

Cites Work

• General state changes in quantum theory
• Quantum learning algorithms for quantum measurements
• A Radon-Nikodym theorem for completely positive maps
• Non-Markovian quantum stochastic processes and their entropy
• Subalgebras of \(C^ *\)-algebras
• An operational approach to quantum probability
• Generalized channels: Channels for convex subsets of the state space
• The Dual of the Haagerup Tensor Product
• Quartic quantum theory: an extension of the standard quantum mechanics
• Complete Characterization of Arbitrary Quantum Measurement Processes
• Radon–Nikodym derivatives of quantum operations
• Theoretical framework for quantum networks
• Barycentric decomposition of quantum measurements in finite dimensions

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