Quantum Networks: general theory and applications

TL;DR

This paper introduces a comprehensive mathematical framework for quantum networks, enabling efficient representation and solution of complex quantum information processing tasks such as tomography, cloning, and transformation learning.

Contribution

It generalizes the Choi isomorphism to represent quantum networks as single positive operators, facilitating analysis and problem-solving in quantum information science.

Findings

Unified formalism for quantum networks

Efficient representation of quantum processes

Application to key quantum information tasks

Abstract

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.