QuTech at the Delft University of Technology and TNO, in collaboration with the European Quantum Internet Alliance, is leading the efforts to establish a quantum Internet and aims at having a proof of concept version, between the cities of Amsterdam, Leiden, Delft and the Hague. The quantum Internet looks a lot like the classical Internet, we have a network of computers and we send data from one computer to another. On the quantum Internet we have quantum computers sending quantum data, quantum bits! On the surface the quantum Internet may look just like the classical Internet but if we dig a little bit deeper we will discover features that some decades ago seemed like science fiction!

In the above figure we see an artists representation of two entangled states shared between two diamonds. A key ingredient for the realization of entanglement distillation. Taken from qutech.nl or [7]. Recently the research group of Ronald Hanson in Delft in collaboration with researchers from Oxford managed to distil a strong entangled link by combining multiple weaker quantum links into one. This method is essential to realize a trustworthy quantum network between several quantum nodes.

The concept of entanglement is the distinctive feature that allows quantum information to overcome some of the limitations posed by classical information, see also [2]. Entanglement leads to profound experimental consequences like nonlocal correlations: when two distant parties A (Alice) and B (Bob) share quantum information the measurement by A of her state univocally determines the state on the B side. Apparently this implies instant transmission of information, in sharp contrast with Einstein’s relativity. However, to reconcile both facts we must notice that the only way the B side can know about his state (without measuring it) is by receiving a classical communication from the A side, which propagates no faster than the speed of light. For such reasons, entanglement is considered as a resource in quantum information, something that we must have available if we want to take advantage of the new communication possibilities exhibited by quantum protocols.

In the following video a short introduction to the quantum internet by Stephanie Wehner.

#### The role of quantum synchronization

An important application of quantum synchronization is to provide effective quantum correlation for quantum information processing. In a previous article we describe the relationship between quantum synchronization and entanglement.

The phenomenon of quantum synchronization on complex networks have so far remained almost unexplored. In the recent work [4] a first step is made by finding an opto-mechanical implementation, which is shown in the figure below.

This design allows us to obtain quantum synchronization between two completely different oscillators. In the figure above the cavities are the carriers of the quantum states. The electro-optomechanical systems are coupled via phonon tunneling and a linear resistor. The Fabry-Pérot cavities contain a charged oscillator which couples with the cavity via a linear optomechanical interaction.

The synchronization mechanisms discussed in [4] are as follows:

Circuit coupling controls subsystems that eventually reach the same effective frequency, which means two subsystems evolve under the same dynamic equation. If this is accomplished, the phonon coupling will offset the initial phase difference between the systems. In [4] many details are provided that show how well quantum synchronization is actually established. Measures like the fidelity show that only in the case, when the systems are both coupled classically and quantum mechanically genuine quantum synchronization can be demonstrated.

The next challenge is to extend this synchronization to more general complex networks. So far this has only been checked for relatively small networks, but the results are very promising. For example, it was found in [4] that in small world network consisting of only 12 nodes, synchronization is easily achieved and the fidelity can stabilize at 100% for very long times. Moreover, it turns out that even when the topology is changing with time identical states can be transmitted in this network, without need for additional controls, which is a feature that is highly beneficial for quantum communication.

In this case one effectively describes the quantum state sharing as interdependent communication between two network nodes. This is no longer true for scale free networks where additional control mechanism are required as the whole network needs to be synchronized at the same time, that is, a scale free network describes an information diffusion process.

In the following video Stephanie Wehner shares some ideas on the quantum internet. Stephanie Wehner is an Antoni van Leeuwenhoek Professor at QuTech, Delft University of Technology, where she leads the Quantum Internet efforts. Her passion is the theory of quantum information in all its facets, and she has written numerous scientific articles in both physics and computer science.

[1] Witthaut, Wimberger, Burioni and Timme, Classical synchronization indicates persistent entanglement in isolated quantum systems, Nature Communications (2017).

[2] A. Galindo and M. A. Mart'in-Delgado, Information and computation: Classical and quantum aspects, Reviews of modern physics 74 (2002).

[3] H.J. Krimble, The quantum internet, Nature 453 (2008).

[4] Li, Li and Song, Quantum synchronization and quantum state sharing in an irregular complex network, Physical Review E (2017).

[5] Distillatie brengt quantum internet een stap dichterbij. TuDelft

[6] Quantum Internet and Networked Computing. QuTech

[7] N. Kalb, A. A. Reiserer, P. C. Humphreys, J. J. W. Bakermans, S. J. Kamerling, N. H. Nickerson, S. C. Benjamin, D. J. Twitchen, M. Markham, R. Hanson*, *Entanglement distillation between solid-state quantum network nodes*, Science *(2017).