Theoretical framework for quantum networks

TL;DR

This paper develops a comprehensive theoretical framework for quantum networks, encompassing all transformations like cloning and measurement, using quantum combs and link products, and introduces the universality of quantum memory channels.

Contribution

It introduces a unified framework for quantum networks based on quantum combs and link products, and proves the universality of quantum memory channels for all admissible transformations.

Findings

Framework covers all quantum network transformations

Universality of quantum memory channels proven

Open problem posed for nonquantum theories

Abstract

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