About me

I am a Senior Scientist at the Institute of Atomic and Subatomic Physics (Atominstitut) of TU Wien, where I am leading the Entanglement and Quantum Computing Theory (EntaQCT) group, which is part of the Research Unit Quantum Optics and Quantum Information (QuOI).
My team is funded by the Austrian Science Fund (FWF) through the Stand-Alone project "Entanglement-Based Certification of Quantum Technologies" (EBCQT, project number P 36478-N) and by the Austrian Federal Ministry of Education, Science and Research via the Austrian Research Promotion Agency (FFG) through the flagship project "High-Performance integrated Quantum Computing" (HPQC, project number FO999897481), both funded by the European Union – NextGenerationEU.
My research interests lie in the overlap of quantum information & computation with  quantum optics, quantum metrology, and quantum thermodynamics. Recently, I have been interested in entanglement theory, entanglement detection and certification in practical scenarios, and I have been investigating the connections between resources for quantum computation, quantum metrology, and quantum thermodynamics. See the Research Section of my homepage for more details.

I studied physics at the University of Vienna, where I completed my physics diploma in the particle-physics group of Reinhold A. Bertlmann. I then went for a PhD to the University of Nottingham in the UK, followed by postdocs in Innsbruck (in the group of Hans J. Briegel) and at the Institute for Quantum Optics and Quantum Information - IQOQI Vienna (in the group of Marcus Huber).

Apart from direct research activities, I am involved with teaching, peer-review, and am an editor at the community-run open-access journal Quantum. At TU Wien I serve as a Mentor for Responsible Research Practices and as the Chairman of the Curriculum Commission for the Master's Programme Quantum Information Science and Technology (QIST).
Contact
Nicolai Friis
Senior Scientist
Institute of Atomic and Subatomic Physics (Atominstitut) TU Wien
Stadionallee 2
1020 Vienna, Austria
E-mail: nicolai.friis@tuwien.ac.at

News

In a recent joint talk with Otfried Gühne in the qmeets seminar series I had the pleasure of telling the audience about one of my favourite topics: multipartite entanglement–specifically, on the intricate aspects of identifying the pertinent resources in scenario where multiple copies of states are distributed. I had a lot of fun, many thanks to the organizers, Tobi Haas, Mauro D’Achille, Daniele Iannotti, and Krish Karthikeyan, for having us!
I had the pleasure to collaborate with the team of Hui-Tian Wang in Nanjing, in particular, I want to highlight Xi-Lin Wang as well as Xiaoqin Gao. In our work, recently published in Nature Photonics, we realized the (as far as I am aware) first entangling gate between two four-dimensional quantum systems encoded in the orbital angular momentum of two photons. If you want to know more, please read our paper, or have a look at the coverage in, e.g., phys.org (in English) or from the Austrian Press Agency (in German). And, once again, thanks to the fantastic Alexander Rommel for creating the stunning illustration.
In our latest paper [Li, Dai, Muñoz-Arias, Reuer, Huber, Friis, Nat. Commun. 17, 1707 (2026), arXiv:2504.21076] we investigate the detection of genuine multipartite entanglement in systems where only restricted sets of measurements can be carried out, for instance, only on certain connected groups of qubits in a graph structure. In our study, we encountered some mysterious graphs that we felt resembled the head and tails of a certain Lovecraftian cosmic entity... if that has piqued your interest, have a look at our paper, if you dare.
Picture
Image credit: Christian Murzek 2018
Entanglement is a form of correlation that is "stronger" than classical correlations in the sense that correlations are equally strong in infinitely many pairs of bases. But how strong do correlations have to be in any arbitrary given pair of bases to conclude that the system is entangled, or even high-dimensionally entangled? In our latest paper [npj Quantum Inf. 11, 50 (2025)] we answer this question quantitatively, providing (amongst other things) a bound for correlations measured in arbitrary bases for states with any fixed Schmidt number, providing a practical way of certifying the latter that in principle works for any choice of bases.
In our latest publication we report on a somewhat unusual experiment: to demonstrate the robustness of their setup, our experimental colleagues installed a Bell experiment on board of an airplane that subsequently went on a parabola flight. Read about this exciting experiment defying gravity in Quantum 8, 1256 (2024).

A press summary in English can be found here.

Press coverage in Austrian news (in German): derStandard
Quantum computing heavily employs qubits – two-dimensional quantum systems – as carriers of information, yet, physics usually offers many more dimensions. In our latest paper, now published in Quantum 7, 1141 (2023), we sketch some pathways to exploiting higher dimensions to reduce the overheads for quantum computation.
Our textbook "Modern Quantum Theory - From Quantum Mechanics to Entanglement and Quantum Information", published by Oxford University Press, is now out in print and as e-book!

The more than 1000 pages provide a fully referenced introduction to quantum mechanics and a treatment of (the basics of) modern quantum information theory, which we hope will be useful to students, researchers and (university-level) teachers alike.

The cover was created by the extremely talented Alexander Rommel, https://aerroscape.de
In our latest article [Simon Morelli, David Sauerwein, Michalis Skotiniotis & NF, Quantum 6, 722 (2022)], we discuss how entanglement distribution protocols in noisy quantum networks can be improved by embedded parameter-estimation subroutines. Have a look!
In our paper "Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation" [Yamasaki, Morelli, Miethlinger, Bavaresco, Friis, Huber, Quantum 6, 695 (2022)] we show that, unlike bipartite entanglement, genuine multipartite entanglement (GME) can be activated in the sense that several copies of states that are not GME individually, can become GME jointly. In this new entanglement characterisation paradigm beyond single copies, we prove that there are states for which 2 copies are enough to activate GME, but there are also some for which only 3 copies suffice. Moreover, we show that even biseparable states with only undstillable entanglement can be used to activate GME.
On March 11th, 2022 I held my habilitation colloquium at the Faculty of Physics of the University of Vienna, completing the requirements for habilitation. The slides of the presentation can be downloaded here (as pdf), and my habilitation thesis entitled "Thermodynamic Considerations in Quantum Information Processing" can be downloaded here.
I am very happy to announce that I joined the Editorial Board of Quantum. I am extremely grateful for this opportunity to help shape and grow the quantum community, and humbled to be entrusted with such a responsibility, looking forward to many great manuscripts!
In our recent paper `Entanglement Quantification in Atomic Ensembles', just published in Phys. Rev. Lett. 127, 010401 (2021), we consider families of entanglement criteria based on operator variances and use these to derive lower bounds for two relevant entanglement measures. This yields a practical method for quantifying entanglement in realistic experimental situations, which we demonstrate by applying our method to quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates, using data from Fadel et al., Science 360, 409 (2018) and Schmied et al., Science 352, 441 (2016).

(Image credit: Alexander Rommel, © IQOQI Vienna)
Two years after our experimental demonstration of quantum-enhanced decision making in quantum-classical (quantum hardware+classical learning environment) reinforcement learning [Sriarunothai, et al., Quant. Sci. Techn. 4, 015014 (2019)], we have now
demonstrated a learning speed-up in fully quantum-quantum reinforcement learning in an international collaboration led by Valeria Saggio in Philip Walther's group: the paper is out in Nature and on the arXiv: Saggio et al.,Experimental quantum speed-up in reinforcement learning agents, Nature 591, 229-233 (2021) [arXiv:2103.06294]. (image credit © Rolando Barry, Universität Wien)

More information and media coverage:Popular summary (in German, Austrian Academy of Science)
Articles in New Scientist and phys.org (English)
Austrian news (in German): standard.at
In our new paper just out in PRX [Schwarzhans, Lock, Erker, Friis, Huber, Phys. Rev. X 11, 011046 (2021)], we investigate autonomous quantum clocks, which harness the entropic flow to keep track of time. We separate the operation of such a clock into two tasks: (i) an irreversible process that results in `tick' events, and (ii) a clockwork that structures the entropic flow by concentrating the probability for such ticks to occur within well defined narrow time intervals. We identify this second process, which we call autonomous temporal probability concentration (ATPC), as being crucial for obtaining a clock of high quality. We study the resource requirements for APTC and the trade-offs between these resources. (Image credit: IQOQI Vienna/Harald Ritsch)
Parameter estimation is a taks that is often studied in the "local" regime, where small flucutations in a local neighbourhood of some already well-known parameter value are being estimated. There, methods based on the Cramër-Rao bound apply. In our new paper [Morelli, Usui, Agudelo, Friis, Quantum Sci. Technol. 6, 025018 (2021)], we investigate a different parameter estimation paradigm: Bayesian estimation, where initial knowledge is updated based on newly obtained information. We study Bayesian estimation problems, including the esitmation of displacements, phases, and squeezing, using practically easily reliazable strategies based on Gaussian probe states and measurements.
In our latest paper just published in Nature [Erhard, Poulsen Nautrup et al., Entangling logical qubits with lattice surgery, Nature 589, 220--224 (2021), arXiv:2006.03071], we report on the experimental realization of lattice surgery between two topologically encoded qubits in a 10-qubit ion trap. In particular, we demonstrate entanglement between two logical qubits encoded in two 4-qubit surface codes and we implement logical state teleportation between them.

Press release from IQOQI Innsbruck (English),
Phys.org (English), Physics World (English)
Austrian news (in German): ORF & der Standard
In our newly published paper "High-Dimensional Pixel Entanglement: Efficient Generation and Certification" [Herrera Valencia et al., Quantum 4, 376 (2020)] in collaboration with BBQ Lab at Heriot-Watt, we present new methods for creating and certifying high-dimensional entanglement between spatial modes of light. We are able to certify record values for entanglement of formation (4.0±0.1 ebits in local dimension 31) and Schmidt number (55 in dimension 97).

Press release from IQOQI Vienna (English),
Austrian news (in German): der Standard
Starting October 2020, I took on the responsibility of providing quality control and copy-editing for Quantum Views, invited perspective pieces for selected articles published in Quantum, the open-access peer-reviewed journal for quantum science and related fields.
In our new paper "Teleporting quantum information encoded in fermionic modes", just out in Physical Review A 101, 052326 (2020), we take a closer look at the influence of superselection rules on teleportation (and what it even means to "teleport") using fermionic mode entanglement.
The notion of measurement forms an integral part of quantum mechanical reasoning. In our paper "Ideal Projective Measurements Have Infinite Resource Costs" [Y. Guryanova, N. Friis, and M. Huber, Quantum 4, 222 (2020)], we show that ideal measurements are impossible and establish a framework for studying non-ideal measurements which can approximate ideal measurements at finite energy cost.
In our latest paper out on the arXiv [H. Poulsen Nautrup, N. Delfosse, V. Dunjko, H. J. Briegel, and N. Friis, Quantum 3, 215 (2019)], we present a reinforcement learning approach for optimizing and adapting quantum error correction codes. In our aproach, agents learn to design good error correction codes that use as few qubits as possible and they are able to transfer their experience from one situation to another.
Thermodynamics implies that measurements are non-ideal and require an input of energy. In our paper `Work estimation and work fluctuations in the presence of non-ideal measurements', we explore the consequences of non-ideal measurements for work estimation [T. Debarba, G. Manzano, Y. Guryanova, M. Huber, and N. Friis, New J. Phys. 21, 113002 (2019), arXiv:1902.08568].
Correlations have an energy cost that we investigate in our new paper: Thermodynamically optimal creation of correlations [F. Bakhshinezhad, F. Clivaz, G. Vitagliano, P. Erker, A. T. Rezakhani, M. Huber, and N. Friis, J. Phys. A Math. Theor. 52, 465303 (2019), arXiv:1904.07942]. In particular, we present mathematical tools for determining the existence of symmetrically thermalizing unitaries necessary saturate entropic bounds on the energy cost of correlations.
Our review "Trade-Off Between Work and Correlations in Quantum Thermodynamics" has been published as a chapter in: Thermodynamics in the Quantum Regime, Chapter 30, edited by F. Binder, L. A. Correa, C. Gogolin, J. Anders, and G. Adesso (Springer 2019) [arXiv:1803.06884].
Picture
Image credit: Christian Murzek 2018
Every wondered about the different worlds inhabited by theorists and experimentalists? Find out more in this wonderful blog post about our new review paper "Entanglement certification from theory to experiment", fresh out in Nat. Rev. Phys. 1, 72-87 (2019).
Our paper entitled "Speeding-up the decision making of a learning agent using an ion trap quantum processor", has now been published in Quantum Science and Technology. We report on a first proof-of-principle experiment demonstrating a quantum speed-up in the deliberation time of quantum learning agents w.r.t. to their classical counterparts [Sriarunothai, Wölk, Giri, Friis, Dunjko, Briegel, Wunderlich, Quant. Sci. Techn. 4, 015014 (2019), arXiv:1709.01366].
 Our experiment & theory collaboration paper "Measurements in two bases are sufficient for certifying high-dimensional entanglement" has appeared online in Nat. Phys. 14, 1032 (2018) [earlier version available at arXiv:1709.07344].

In this work, we develop efficient new techniques for certifying high-dimensional entanglement using measurements in only two bases. We demonstrate the usefulness of this method: we certify 9-dimensional entanglement of two photons entangled in their orbital angular momentum. (Image credit: upper: Mehul Malik, lower: IQOQI Vienna/Harald Ritsch)
The second installment of our investigation of the usefulness and limitations of Gaussian operations in quantum thermodynamics is now available on the arXiv: Precision and Work Fluctuations in Gaussian Battery Charging, has now been published in Quantum 2, 61 (2018).
In a recent collaboration with Innsbruck and Ulm, we have been able track the dynamics of the development of genuine multipartite entanglement in groups of up to 5 neighbours in a chain of 20 fully controlled trapped-ion qubits. The paper hast just been published in Physical Review X [Friis, Marty et al., Phys. Rev. X 8, 021012 (2018)]. (Image credit: IQOQI Innsbruck/Harald Ritsch)

Press release from IQOQI Innsbruck (English),
Phys.org (English), IEEE Spectrum (English)
Austrian news (in German): ORF & der Standard
Our paper on "Flexible resources for quantum metrology", New J. Phys. 19, 063044 (2017) [arXiv:1610.09999], discussing how 2D cluster states can be used as resources for parameter estimation, has been selected by the editors of New Journal of Physics for inclusion in the 'Highlights of 2017' collection.
I have recently joined the International Editorial Board of the Journal of Physics Communications by IoP. The journal is fully open access and is committed to rigorous peer review assessing the scientific quality and ensuring that contributions advance the respective research areas but explicitly allows for the inclusion of negative or null results and replication studies. 
Read about an exciting new method to transfer quantum information between quantum memories and quantum processors in "Fault-tolerant interface between quantum memories and quantum processors" which was just published in Nat. Commun. 8, 1321 (2017) [arXiv:1609.08062].

Press release from the University of Innsbruck (English)
Austrian news (in German): ORF Tirol & der Standard
Phys.org coverage (English)
IEEE Spectrum Article (English)
"Geometry of two-qubit states with negative conditional entropy", our recent paper contrasting a variety of different entanglement detection criteria geometrically, has been published in J. Phys. A: Math. Theor. 50, 125301 (2017) [arXiv:1609.04144].

Update: The article is now fully open access.
Our new article on quantum thermodynamics entitled "Passivity and practical work extraction using Gaussian operations" has been published in the New Journal of Physics: New J. Phys. 18, 113028 (2016) [arXiv:1608.04977].