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Transforming quantum operations: quantum supermaps · Around

2008

Transforming quantum operations: quantum supermaps

Chiribella, G., D'Ariano, G. M., Perinotti, P.

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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.

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G. Chiribella, G. M. D’Ariano, and P. Perinotti, arXiv:0712.1325
Original

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Two causally connected quantum operations are indeed a four-port circuit in which an input device can be plugged, i.e. referring to Fig. 1

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