Quantum Networks: general theory and applications

Understand

In this work we present a general mathematical framework to deal with Quantum Networks, i.e.

• networks resulting from the interconnection of elementary quantum circuits.
• The cornerstone of our approach is a generalization of the Choi isomorphism that allows one to efficiently represent any given Quantum Network in terms of a single positive operator.
• Our formalism allows one to face and solve many quantum information processing problems that would be hardly manageable otherwise, the most relevant of which are reviewed in this work: quantum process tomography, quantum cloning and learning of transformations, inversion of a unitary gate, information-disturbance tradeoff in estimating a unitary transformation, cloning and learning of a measurement device.