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Abstract: We present a framework to treat quantum networks and all possibletransformations thereof, including as special cases all possible manipulationsof quantum states, measurements, and channels, such as, e.g., cloning,discrimination, estimation, and tomography. Our framework is based on theconcepts of quantum comb-which describes all transformations achievable by agiven quantum network-and link product-the operation of connecting two quantumnetworks. Quantum networks are treated both from a constructive point ofview-based on connections of elementary circuits-and from an axiomaticone-based on a hierarchy of admissible quantum maps. In the axiomatic context afundamental property is shown, which we call universality of quantum memorychannels: any admissible transformation of quantum networks can be realized bya suitable sequence of memory channels. The open problem whether this propertyfails for some nonquantum theory, e.g., for no-signaling boxes, is posed.

Author: Giulio Chiribella, Giacomo M. D'Ariano, Paolo Perinotti


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