** Abstract **

We consider entanglement-based quantum networks, where pre-shared multipartite entangled states serve as a resource to fulfill general network requests on demand [1,2]. Such a top-down approach is unique to quantum networks, and offers new possibilities and features such as speeding up network requests, and network optimization independent of the underlying physical structure. The main challenge here is to identify suitable resource states shared between network devices that can be modified by local means such that the desired output state (and hence the desired network functionality) can be guaranteed. This minimizes generation times for target states, and allows for network structures that are independent of physical links, as the resources states can be generated prior to requests and then stored until they are needed.

We present a modular and flexible architecture to achieve this aim [1]. We also provide a stack model for such entanglement-based networks [2], and introduce network protocols at different layers to achieve the desired network configuration and fulfill network requests.  Such entanglement-based networks are independent of the topology of the underlying physical network, which can be utilized to design optimized networks [3] tailored to the desired functionality by choosing appropriate multipartite entangled states to store. This allows one to minimize memory requirements and entanglement, and we present clustering and merging algorithms for such an optimization. 

Finally, we show how to make quantum networks, both standard and entanglement-based, genuine quantum by providing them with the possibility of handling superposed tasks and superposed addressing [4]. This extension of their functionality relies on a quantum control register, which specifies not only the task of the network, but also the corresponding weights in a coherently superposed fashion. This allows one e.g. to prepare superposition of different target states, or to send information among a superposition of different paths. Such an approach can also be utilized in randomized benchmarking of circuits or networks [5], where we develop protocols with increased efficiency and functionality.  A brief overview over other relevant network protocols, such as improved entanglement purification methods [6], transmission of big quantum data in bipartite and multipartite scenarios [7], and delocalized storage of information in quantum networks [8] is also provided. 

References:
[1] A. Pirker, J. Wallnöfer and W. Dür, New J. Phys. 20, 053054 (2018). 
[2] A. Pirker and W. Dür, New J. Phys. 21, 033003 (2019).
[3] J. Miguel-Ramiro, A. Pirker and W. Dür, Optimized quantum networks, in preparation (2021)
[4] J. Miguel-Ramiro, A. Pirker and W. Dür, E-print: arXiv:2005.00020 .  
[5] Jorge Miguel-Ramiro, Alexander Pirker and Wolfgang Dür, Phys. Rev. Research 3, 033038 (2021). 
[6] F. Riera-Sabat, P. Sekatski, A. Pirker and W. Dür, E-print:arXiv:2011.07078 (to appear in PRL).
[7] M. Zwerger, A. Pirker, V. Dunjko, H.J. Briegel and W. Dür, Phys. Rev. Lett. 120, 030503 (2018); 
J. Wallnöfer, A. Pirker, M. Zwerger and W. Dür, Scientific Reports 9, 314 (2019);
[8] Jorge Miguel-Ramiro and W. Dür, New J. Phys. 22, 043011 (2020).

** Speaker bio **

Wolfgang Dür is an Associate Prof. at the University of Innsbruck. He is interested in all aspects of quantum information theory, where he has contributed to various topics, including quantum networks, quantum metrology, measurement-based quantum computation, decoherence and large-scale entanglement, quantum information theory and multipartite entanglement. He is also involved in teacher education, and working on didactic of physics – in particular how to teach the mysteries of quantum mechanics at high-school level. 

During his master thesis he has co-invented the quantum repeater, and worked on various aspects of long-distance quantum communication and quantum networks in the last 20 years, including protocols for entanglement purification and error correction, repeater schemes for bipartite and multipartite systems and network architectures. He is also one of the pioneers of research on multipartite entanglement, with the W-state associated with him, but also with many contributions in the context of graph states and measurement-based quantum information processing, highlighting the improved robustness of such an approach in the context of quantum computation and communication. He is also interested in fundamental aspects of quantum mechanics, including Bell inequalities and the treatment of macroscopic quantum systems, in particular w.r.t. to limitations to prepare, maintain, measure and use such systems. In addition he has contributed to quantum metrology showing how to utilize methods from quantum error correction and quantum control to overcome or reduce the influence of noise and imperfections on sensing of local and non-local quantities.

Research overview:

Publications in refereed journals: >130 (>35 in Phys.Rev.Lett., Nature, Nature Physics)
Citations: >6000 (ISI citation index), h-Index 34; >17600 (Google scholar), h-Index 55

Talks at conferences/workshops: >20

Selected works:
H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller,  Phys. Rev. Lett. 81, 5932 (1998). ``Quantum repeaters: The role of imperfect local operations in quantum communication'' 
W. Dür , G. Vidal and J. I. Cirac, Phys. Rev. A 62, 062314 (2000). ``Three qubits can be entangled in two inequivalent ways'' –  selected as 50th anniversary milestone paper, https://journals.aps.org/pra/50th 
H. J. Briegel, D.E. Browne, W. Dür, R. Raussendorf and M. Van den Nest, Nature Physics 5, Vol. 1, 19-26 (2009). `` Measurement-based quantum computation’’ 
W. Dür, M. Skotiniotis, F. Fröwis and B. Kraus, Phys. Rev. Lett. 112, 080801 (2014). `` Improved quantum metrology using quantum error-correction’’
P. Sekatski, M. Skotiniotis, J. Kolodynski and W. Dür, Quantum 1, 27 (2017); ``Quantum metrology with full and fast quantum control‘‘
M. Zwerger, A. Pirker, V. Dunjko, H.J. Briegel and W. Dür, Phys. Rev. Lett. 120, 030503 (2018). `` Long-range big quantum-data transmission ‘‘
F. Fröwis, P. Sekatski, W. Dür, N.Gisin and N. Sangouard,  Rev. Mod. Phys. 90, 025004 (2018), ``Macroscopic quantum states: measures, fragility and implementations‘‘
A. Pirker and W. Dür, New J. Phys. 21, 033003 (2019), ``A quantum network stack and protocols for reliable entanglement-based networks ‘‘
Andrea López-Incera and Wolfgang Dür. Entangle me!, A game to demonstrate the principles of quantum mechanics, Am. J. Phys. 87, 95 (2019) (Editor's pick).