Here, you can find a list of my publications and preprints. They are sorted in order of appearance on the arXiv (beginning with the latest)
Robust Device-Independent Quantum Key Distribution
Joint work with René Schwonnek, Koon Tong Goh, Ignatius W. Primaatmaja, Ernest Y.-Z. Tan, Valerio Scarani, Charles C.-W. Lim
Device-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. In this work, we close the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. In using two randomly chosen key generating bases instead of one, we show that the noise tolerance of DIQKD can be significantly improved. In particular, the extended feasibility region now covers some of the most recent loophole-free CHSH experiments, hence indicating that the first realisation of DIQKD already lies within the range of these experiments.
Generalized string-nets for unitary fusion categories without tetrahedral symmetry
Joint work with Alexander Hahn
Journal: Physical Review B 102, 115154 (2020)
The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since some additional symmetries for the F-symbols are imposed. In particular, the so-called tetrahedral symmetry is not fulfilled by many interesting unitary fusion categories. In this paper, we present a generalized construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories that works without requiring these additional symmetries. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.
Gauging defects in quantum spin systems: A case study
Joint work with Jacob C. Bridgeman, Alexander Hahn, and Tobias J. Osborne
Journal: Physical Review B 101, 134111 (2020)
The goal of this work is to build a dynamical theory of defects for quantum spin systems. This is done by explicitly giving an exhaustive case study of a one-dimensional spin chain with Vec(Z/2Z) fusion rules, which can easily be extended to more general settings. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. Technically, this is done by employing generalized tube algebra techniques to model the defects in the chain. We illustrate this approach for the Vec(Z/2Z) spin chain, in whose case the resulting dynamical defect model is equivalent to the critical transverse Ising model.
The F-Symbols for the H3 Fusion Category
Joint work with Tobias J. Osborne and Deniz E. Stiegemann
We present a solution for the F-symbols of the H3 fusion category, which is Morita equivalent to the even parts of the Haagerup subfactor. This solution has been computed by solving the pentagon equations and using several properties of trivalent categories.
Training deep quantum neural networks
Joint work with Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J. Osborne, Robert Salzmann, and Daniel Scheiermann
Journal: Nature Communications 11, 808 (2020)
Neural networks enjoy widespread success in both research and industry and, with the advent of quantum technology, it is a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose a truly quantum analogue of classical neurons, which form quantum feedforward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function, providing both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing deep-network optimisation. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.
From categories to anyons: a travelogue
Joint work with Kerstin Beer, Dmytro Bondarenko, Alexander Hahn, Maria Kalabakov, Nicole Knust, Laura Niermann, Tobias J. Osborne, Christin Schridde, Stefan Seckmeyer, Deniz E. Stiegemann
In this paper we provide an overview of category theory, focussing on applications in physics. The route we follow is motivated by the final goal of understanding anyons and topological QFTs using category theory. This entails introducing modular tensor categories and fusion rings. Rather than providing an in-depth mathematical development we concentrate instead on presenting the „highlights for a physicist“.
Entanglement detection by violations of noisy uncertainty relations: A proof of principle
Joint work with Yuan-Yuan Zhao, Guo-Yong Xiang, Xiao-Min Hu, Bi-Heng Liu, Chuan-Feng Li, Guang-Can Guo, René Schwonnek
It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.