Abstract
We develop a local probe to estimate the connectivity of complex quantum networks. Our results show how global properties of different classes of complex networks can be estimated – in quantitative manner with high accuracy – by coupling a probe to a single node of the network. Here, our interest is focused on probing the connectivity, i.e. the degree sequence, and the value of the coupling constant within the complex network. The scheme combines results on classical graph theory with the ability to develop quantum probes for networks of quantum harmonic oscillators. Whilst our results are proof-of-principle type, within the emerging field of quantum complex networks they may have potential applications for example to the efficient transfer of quantum information or energy or possibly to shed light on the connection between network structure and dynamics.
Highlights
While the study of classical complex networks has enjoyed considerable interest throughout the last 20 years[1,2,3], the study of interacting quantum systems as quantum complex networks has only recently started to emerge[4,5]
Networks are any systems that can be thought of as being composed of many interacting or otherwise related subsystems or entities. This includes an immense variety of large complex systems such as acquaintance networks[18], the global shipping network[19] and food webs in an ecosystem[20,21], and microscopic ones like metabolic processes in a cell[22,23] and light-harvesting complexes[24]
The ability to capture the essential features of so many different systems of interest makes network theory a powerful tool
Summary
While the study of classical complex networks has enjoyed considerable interest throughout the last 20 years[1,2,3], the study of interacting quantum systems as quantum complex networks has only recently started to emerge[4,5]. Much of its power stems from reducing a complicated system into an abstract graph composed of nodes connected by links This can be studied independently of what the physical network is and revealing, e.g., important information on mechanisms influencing the construction and evolution of these complex systems. An important problem in network theory is the extraction of information about the network when only a small subset of its constituents can be accessed This has been considered in the quantum case, and it has been shown that, provided one has suitable prior knowledge of the network, it is possible to determine several of its properties indirectly using a probe system, such as the network state[25], temperature[26,27], and coupling strengths between nodes[28,29]. As an example of this type of system, we use a network of identical quantum harmonic oscillators interacting with spring-like couplings of constant magnitude[9,31]
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