Transforming quantum operations: Quantum supermapsG. Chiribella, G. M. D'Ariano and P. Perinotti
QUIT Group, Dipartimento di Fisica "A. Volta" and CNISM - via Bassi 6, 27100 Pavia, Italy, EU
received 1 April 2008; accepted in final form 9 June 2008; published August 2008
published online 11 July 2008
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
03.67.-a - Quantum information.
03.65.-w - Quantum mechanics.
03.65.Ta - Foundations of quantum mechanics; measurement theory.
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