One of the main research interests within our research area is the study of entanglement, a form of correlation between quantum systems that is in some sense stronger than correlations between classical systems can be. For entangled states correlations between measurement outcomes of two or more parties can be equally strong for suitable complementary local observables. Entanglement is a resource for a variety of quantum-communication protocols such as quantum teleportation or dense coding and lies at the heart of many applications in quantum technologies (e.g., entanglement-based quantum key distribution based on the Ekert-91 protocol). At the same time, the presence of entanglement is necessary for the violation of Bell inequalities (a phenomenon commonly referred to as `non-locality’), which is both of foundational interest but also of significance for device-independent approaches to certification (see, e.g., [1] for a review, or Chapters 15 to 18 of [2] for a detailed introduction).

The particular focus of our activities in this direction lies on exploring the theoretical and practical aspects of the characterization, detection, and quantification of entanglement in high-dimensional, infinite-dimensional (continuous-variable), and in multipartite settings. In the area of high-dimensional entanglement, we are exploring different criteria for certifying the entanglement dimensionality via a quantity called the Schmidt number, see, e.g., our recent work in [3-6]. On the side of multipartite entanglement, we have recently been investigating the phenomenon of multi-copy activation of genuine multipartite entanglement [7] and its occurrence in infinite-dimensional systems [8], and we have also studied the distribution of entanglement in networks assisted by parameter-estimation techniques [9]. From a fundamental mathematical point of view, we are interested in exploring the geometric structure of the state space [10,11].

In addition, we are engaged with connecting theoretical results to practical applications of entanglement certification in a variety of platforms, ranging from ultracold atomic ensembles [12], photon pairs entangled in their spatial (orbital angular momentum) [13,14] and in their energy-time [15] degrees of freedom, to trapped-ion quantum simulators [16].

References:

[1] Nicolai Friis, Giuseppe Vitagliano, Mehul Malik, and Marcus Huber, Entanglement certification from theory to experiment, Nat. Rev. Phys. 1, 72 (2019) [arXiv:1906.10929]

[2] Reinhold Bertlmann and Nicolai Friis, Modern Quantum Theory: From Quantum Mechanics to Entanglement and Quantum Information, Oxford University Press, Oxford, U.K., 2023. ISBN: 9780199683338; DOI: 10.1093/oso/9780199683338.001.0001

[3] Shuheng Liu, Matteo Fadel, Qiongyi He, Marcus Huber, and Giuseppe Vitagliano, Bounding entanglement dimensionality from the covariance matrix, Quantum 8, 1236 (2024) [arXiv:2208.04909]

[4] Shuheng Liu, Qiongyi He, Marcus Huber, Otfried Gühne and Giuseppe Vitagliano, Characterizing entanglement dimensionality from randomized measurements, PRX Quantum 4, 020324 (2023) [arXiv:2211.09614]

[5] Shuheng Liu, Qiongyi He, Marcus Huber, Giuseppe Vitagliano, A nonlinear criterion for characterizing high-dimensional multipartite entanglement, preprint arXiv:2405.03261 [quant-ph] (2024)

[6] Nicky Kai Hong Li, Marcus Huber, Nicolai Friis, High-dimensional entanglement witnessed by correlations in arbitrary bases, preprint arXiv:2406.04395 [quant-ph] (2024)

[7] Hayata Yamasaki, Simon Morelli, Markus Miethlinger, Jessica Bavaresco, Nicolai Friis, and Marcus Huber, Activation of genuine multipartite entanglement: beyond the single-copy paradigm of entanglement characterisation, Quantum 6, 695 (2022), [arXiv:2106.01372]

[8] Klára Baksová, Olga Leskovjanová, Ladislav Mišta Jr., Elizabeth Agudelo, and Nicolai Friis,
Multi-copy activation of genuine multipartite entanglement in continuous-variable systems,
preprint arXiv:2312.16570 [quant-ph] (2023).

[9] Simon Morelli, David Sauerwein, Michalis Skotiniotis, and Nicolai Friis, Metrology-assisted entanglement distribution in noisy quantum networks, Quantum 6, 722 (2022) [arXiv:2110.15627]

[10] Nicolai Friis, Sridhar Bulusu, and Reinhold A. Bertlmann, Geometry of two-qubit states with negative conditional entropy, J. Phys. A: Math. Theor. 50 125301 (2017) [arXiv:1609.04144]

[11] Simon Morelli, Christopher Eltschka, Marcus Huber, and Jens Siewert, Correlation constraints and the Bloch geometry of two qubits, Phys. Rev. A 109, 012423 (2024) [arXiv:2303.11400]

[12] Matteo Fadel, Ayaka Usui, Marcus Huber, Nicolai Friis, and Giuseppe Vitagliano, Entanglement quantification in atomic ensembles, Phys. Rev. Lett. 127, 010401 (2021), [arXiv:2103.15730]

[13] Jessica Bavaresco, Natalia Herrera Valencia, Claude Klöckl, Matej Pivoluska, Paul Erker, Nicolai Friis, Mehul Malik, and Marcus Huber, Measurements in two bases are sufficient for certifying high-dimensional entanglement, Nat. Phys. 14, 1032 (2018) [arXiv:1709.07344]

[14] Natalia Herrera Valencia, Vatshal Srivastav, Matej Pivoluska, Marcus Huber, Nicolai Friis, Will McCutcheon, and Mehul Malik, High-Dimensional Pixel Entanglement: Efficient Generation and Certification, Quantum 4, 376 (2020) [arXiv:2004.04994]

[15] Sebastian Ecker, Frédéric Bouchard, Lukas Bulla, Florian Brandt, Oskar Kohout, Fabian Steinlechner, Robert Fickler, Mehul Malik, Yelena Guryanova, Rupert Ursin, and Marcus Huber, Overcoming Noise in Entanglement Distribution, Phys. Rev. X 9, 041042 (2019) [arXiv:1904.01552]

[16] Nicolai Friis, Oliver Marty, Christine Maier, Cornelius Hempel, Milan Holzäpfel, Petar Jurcevic, Martin B. Plenio, Marcus Huber, Christian Roos, Rainer Blatt, and Ben Lanyon, Observation of Entangled States of a Fully Controlled 20-Qubit System, Phys. Rev. X 8, 021012 (2018) [arXiv:1711.11092]