#### Friday 4 June

### Chair

**Harry Buhrman – Center for Mathematics and Computer Science & University of Amsterdam****Jop Briët – Center for Mathematics and Computer Science**

The track Quantum Networks is jointly organised with the Gravitation programme Quantum Software Consortium

This track is about network phenomena in quantum information science, a field whose main aim is to explore computational and information-theoretic aspects of quantum mechanics. Key examples include quantum algorithms for classical problems, for instance to study large graphs, networks of quantum systems, where strange interactions connect nodes of separated quantum systems, communication networks featuring quantum-enhanced channels or channels for transmitting quantum information itself, and computational complexity theory under the presence of quantum devices and agents.

These topics enjoy lively interactions with a broad range of mathematical areas, including combinatorics, functional analysis, algebra and probability. Some of the state of the art on these themes will be presented by world experts.

### Speakers

**David Peréz-García**

Universidad Complutense de Madrid

*Geometry of Banach spaces: a new route towards Position Based Cryptography*

**Abstract**: In the field of position based cryptography one aims to develop cryptographic tasks using the geographical position of an agent as its only credential. Once the agent proved to the verifier that he/she is in fact at the claimed position, they interact considering the identity of the agent as guaranteed. This proposal is appealing for practical applications and it is also of fundamental interest since it presents a way to prevent man-in-the-middle attacks without the need of a secure private channel. Furthermore, since the study of position based cryptography entered into the quantum domain approximately a decade ago, beautiful and striking connections were established with topics ranging from classical complexity theory to the AdS/CFT holographic correspondence. In this talk, I will present a new connection with geometric functional analysis that allows us to use a Sobolev-type inequality due to Pisier for vector-valued functions on the boolean hypercube. Using it as a key tool, we will provide new lower bounds on the entanglement consumption needed to break position based cryptography.

(Joint work with Marius Junge, Aleksander M. Kubicki and Carlos Palazuelos.)

**Sophie Hermans**

TU Delft

*Realization of a multinode quantum network*

**Abstract**: A future quantum internet can unlock fundamentally new technologies by sharing entangled states across the nodes of the network. In the past decade, many buildings blocks of such a network have been demonstrated. Recently we have reached a new milestone; the experimental realization of a multinode quantum network.

During this talk, I will discuss why a quantum internet or quantum networks are interesting. I will explain one experimental implementation (Nitrogen-vacancy centres in diamond), share our results on this world’s first quantum network and talk about challenges for scaling up these networks.

*Photo credits: Inge Hoogland voor Faces of Science/NEMO Kennislink*

**Jelmer Renema**

Twente University

title and abstract: to be announced

**Debbie Leung**

University of Waterloo/Perimeter Institute for Theoretical Physics

*Capacity Approaching Coding for Low Noise Interactive Quantum Communication*

**Abstract: **We consider an arbitrary two-party interactive quantum communication protocol P of n noiseless quantum messages. We provide an interactive protocol P’ using n(1+\Theta(\sqrt(e)) messages of which a fraction e can be corrupted adversarially. The protocol P’ simulates P with failure probability vanishing exponentially in ne.

In this talk, we will describe the problem in detail, why traditional quantum error correcting codes cannot be used, summarize Haeupler’s solution for the analogous classical problem, and several quantum twists required to adapt Haeupler’s solution to the quantum setting.

Joint work with Nayak, Shayeghi, Touchette, Yao, and Yu.

**Laura Mancinska**

QMATH, University of Copenhagen

**Quantum isomorphism is equivalent to equality of homomorphism counts from planar graphs**

**Abstract**: Over 50 years ago, Lovász proved that two graphs are isomorphic if and only if they admit the same number of homomorphisms from any graph [Acta Math. Hungar. 18 (1967), pp. 321–328]. In this talk we will see that two graphs are quantum isomorphic if and only if they admit the same number of homomorphisms from any planar graph.