Máté Farkas


Research groups: Quantum Information Theory



I’m a physics graduate from the Budapest University of Technology and Economics, where I wrote my master’s thesis on a certain type of quantum error correction codes. Later, I joined the group of Marcin Pawlowski in Gdansk for my PhD studies, where I started working on quantum certification techniques. During this time I started many international collaborations (both with theoretical and experimental groups) and published works on the certification of quantum measurements (but also on quantum random number generation, measurement incompatibility and quantum error correction codes), which I also presented at various international conferences. During my PhD, I was refereeing for journals, and in the last year I was the chair organiser of an international conference.

After graduating, I joined the Quantum Information Theory group of Antonio Acín at ICFO, as a post-doctoral researcher. As part of the shift of my research focus to certification techniques based on Bell nonlocality, I started working on device-independent quantum key distribution. This project brought me new international collaborations and I also started co-supervising a PhD student. I also initiated many other projects—mostly related to Bell nonlocality—with various members of the group, and co-supervised undergraduate students. Currently I keep working on these projects and exploring the limitations of quantum certification within Bell nonlocality.


Bell nonlocality and quantum certification

In recent decades it was shown that using quantum mechanical systems to process information can be advantageous over classical information processing. Therefore, in principle one might construct an information processing device (a communication device, or even a computer) that cannot be efficiently simulated using classical devices (such as a standard computer). The natural question then arises: how can one be certain of the correct functioning of such quantum devices, having only access to classical resources?

A partial answer lies in the connection between the aforementioned quantum advantage and the phenomenon called “Bell nonlocality”, that is, the fact that certain multipartite measurement statistics cannot be explained by classical means. Beyond this fundamental observation, Bell nonlocality in some cases allows us to recover a full quantum mechanical description of a multipartite experiment, based solely on the observed measurement statistics, that is, on classical information.

In this project, I apply certification techniques based on Bell nonlocality to various scenarios. Such certification techniques allow us to prove the security of certain quantum cryptographic protocols, and this security is guaranteed simply by the laws of quantum theory. Using these tools, I will investigate the role of entanglement in quantum key distribution protocols. Furthermore, I will attempt to devise experimentally relevant (noise-tolerant) certificates for arbitrary high-dimensional bipartite quantum states.

On the more fundamental side, I will develop a rigorous connection between Bell scenarios, and so-called “contextuality scenarios”. While Bell scenarios consider measurements on a multipartite system, contextuality scenarios model “prepare-and-measure” experiments, with various system preparation and measurement stages. These two scenarios might seem very different at first sight, but perhaps surprisingly, there is an intrinsic connection between them. In this project, I will develop the precise mathematical correspondence between the two scenarios, and using this correspondence, I will translate results from the well-developed field of Bell nonlocality to the perhaps less explored area of contextuality.

Last, I will relate Bell nonlocality to a purely mathematical problem (albeit relevant in quantum information theory): the existence of so-called mutually unbiased bases (MUBs). These are highly symmetric bases in complex Hilbert spaces, and the corresponding quantum measurements are widely useful across various quantum information processing protocols. Despite their usefulness and the large amount of research on the topic, it is still unknown how many pairwise MUBs exist in composite dimensions. To tackle this long-standing open problem, I will use Bell inequalities recently found by me and my collaborators that are maximally violated using MUB measurements (if they exist). I will use and develop techniques for bounding Bell inequality violations in order to tackle the MUB problem, and potentially get new insight into the structure of the problem through the lens of Bell inequalities.

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