Unveiling noiseless clusters in complex quantum networks

Roberta Zambrini,Víctor M Eguíluz,Konstantin Klemm,Albert Cabot,Sabrina Maniscalco,Fernando Galve

doi:10.1038/s41534-018-0108-9

Abstract

The transport and storage of quantum information, excitations, and entanglement, within and across complex quantum networks is crucially affected by the presence of noise induced by their surroundings. Generally, the interaction with the environment deteriorates quantum properties initially present, thus limiting the efficiency of any quantum-enhanced protocol or phenomenon. This is of key relevance, for example, in the design of quantum communication networks and for understanding and controlling quantum harvesting on complex systems. Here, we show that complex quantum networks, such as random and small-world ones, can admit noiseless clusters for collective dissipation. We characterize these noiseless structures in connection to their topology addressing their abundance, extension, and configuration, as well as their robustness to noise and experimental imperfections. We show that the network degree variance controls the probability to find noiseless modes and that these are mostly spanning an even number of nodes, like breathers. For imperfections across the network, a family of quasi-noiseless modes is also identified shielded by noise up to times decreasing linearly with frequency inhomogeneities. Large noiseless components are shown to be more resilient to the presence of detuning than to differences in their coupling strengths. Finally, we investigate the emergence of both stationary and transient quantum synchronization showing that this is a rather resilient phenomenon in these networks.

Highlights

The growing experimental ability in the design, control, and probe of ever larger and increasingly complex coherent quantum systems has recently fueled a newly emerging field combining tools and approaches of complex networks theory with quantum information theory
Several questions have been raised and investigated in this framework: can we exploit quantum correlations to improve security in network communication?7,8,17–19 Does quantum coherence play a role in excitation transfer through networks?21,25,26 Can we use a local quantum probe to extract global information on a complex quantum network?28–30 Can we use complex quantum networks as quantum simulators of nontrivial open quantum systems?28,30,31 How do emergent phenomena known in classical complex networks arise into the quantum regime
We consider a model of interacting quantum harmonic oscillators with linear interactions, so our system belongs to the second class of complex quantum networks as described above

Summary

Introduction

The growing experimental ability in the design, control, and probe of ever larger and increasingly complex coherent quantum systems has recently fueled a newly emerging field combining tools and approaches of complex networks theory with quantum information theory. This cross-disciplinary field aims at understanding static and dynamical properties of complex quantum networks in relation to their topology. Several questions have been raised and investigated in this framework: can we exploit quantum correlations to improve security in network communication?7,8,17–19 Does quantum coherence play a role in excitation transfer through networks?21,25,26 Can we use a local quantum probe to extract global information on a complex quantum network?28–30 Can we use complex quantum networks as quantum simulators of nontrivial open quantum systems?28,30,31 How do emergent phenomena known in classical complex networks arise into the quantum regime?32–35

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Conclusion