#### Research interest

I also carried out research in several different topics in statistical physics, inference theory and condensed matter physics. My Ph.D. was on the statistical physics of inference problems with applications in cancer research, supervised by Prof. Johannes Berg at the Institute for Theoretical Physics, University of Cologne (Cologne, Germany). I also enjoyed studying the quasi-relativistic physics of graphene with Prof. V. Lien Nguyen at Hanoi Institute of Physics (Hanoi, Vietnam), and then with Prof. Markus Müller at the International Center for Theoretical Physics (Trieste, Italy).

#### Publications

*Quantum Physics and Quantum Information*

- Jonathan Steinberg, H. Chau Nguyen, and Matthias Kleinmann,
*"Minimal scheme for certifying three-outcome qubit measurements in the prepare-and-measure scenario,"*, arXiv:2105.09925 (2021). We propose a scheme which can be considered as minimal to verify that a quantum measurement of three outcomes has been performed, i.e., it cannot be simulated by somewhat cheaper measurements of two outcomes. - Xiao-Dong Yu, Timo Simnacher, Nikolai Wyderka, H. Chau Nguyen, and Otfried Gühne,
*"Complete hierarchy for the quantum marginal problem"*, Nature Communication**12**1012 (2021). We are concerned with the existance of a multi-partite quantum state with known marginals on subsets of the parties. Importantly, in various applications the state is required to be pure, thus the problem is in fact non-convex. Yet we show that one can construct a hierarchy of semi-definite programs for the marginal problem, which is complete in the sense that the problem is completely solved at a sufficiently high level in the hierachy. - Xiao-Dong Yu, Timo Simnacher, H. Chau Nguyen, and Otfried Gühne,
*"Quantum-inspired hierarchy for rank-constrained optimisation,"*arXiv:2012.00554 (2020). We show that the techniques of entanglement theory can be used to tackle nonlinear mathematical optimisation problems. - H. Chau Nguyen and Otfried Guehne
*"Some quantum measurements with three outcomes can reveal nonclassicality where all two-outcome measurements fail"*, Phys. Rev. Lett.**125**230402 (2020). We show by means of explicit examples that there are situations where quantum correlations are hidden to any measurements with two outcomes, but can be detected by just few measurements with more outcomes. This shows that the number of outcomes of measurements play an important role in exploiting quantum information and measurements with more outcomes are sometimes indispensible. - Jonathan Steinberg, H. Chau Nguyen, and Matthias Kleinmann
*"Quaternionic quantum theory admits universal dynamics only for two-level systems"*, J. Phys. A: Math. Theor.**53**375304 (2020). We further limit the possibility of building quantum mechanics based on quaternions instead of complex numbers. Essentially, we show that it is difficult, except for low dimensional systems, to interpret the generator of time evolution as an energy observable in quaternionic quantum mechanics. - H. Chau Nguyen, Sébastien Designolle, Mohamed Barakat, and Otfried Gühne,
*"Symmetries between measurements in quantum mechanics,"*, arXiv:2003.12553 (2020). Using the concept of discrete bundles we develop a fully general framework to work with symmetry of a set of quantum measurements. This allows us to systemtise many known characterisations of frequently considered measurement sets, as well as to construct new sets of measurements with novel properties. - H. Chau Nguyen and Otfried Guehne
*"Quantum steering of Bell-diagonal states with generalized measurements"*, Phys. Rev. A**101**042125 (2020). Admiting a simple exact condition for being steerable with projective measurements, Bell diagonal states are rather special and somewhat mysterious with regard to quantum steering. Here we add one more mystery to the states by showing that they also allows a simple condition for being unsteerable with POVMs by an extension of the so-called Barrett construction. - Qiang Zeng, Jiangwei Shang, H. Chau Nguyen, and Xiangdong Zhang
*"Reliable experimental certification of oneway Einstein-Podolsky-Rosen steering,"*arXiv:2010.13014 (2020) . It is curious that the interesting phenomenon of oneway steering is somewhat easier to realised in higher dimension, but difficult to do so in low dimensions. Realising that existing experiments for genuine qubit systems still commits loopholes, we redo the experiment in this setting. - Roope Uola, Ana C. S. Costa, H. Chau Nguyen and Otfried Guehne
*"Quantum steering"*, Rev. Mod. Phys.**92**15001 (2020). We (eventually) complete a review of quantum steering. Basics concepts, detection methods, connections and applications are reviewed. Some interesting open problems are enumerated. - H. Chau Nguyen, Huy-Viet Nguyen and Otfried Guehne,
*"The geometry of Einstein-Podolsky-Rosen correlations"*, Phys. Rev. Lett.**122**240401 (2019). We finally manage to get a solution for the problem of determining the steerability of a given bipartite state; the current description is limited to two-qubit states and projective measurements, but generalisation is under way. As a "by-product", we test the equivalence between POVMs and PVMs in steering*arbitrary*two-qubit states and find ourselves surprised that they seem to be equivalent in even certain strong sense! I have always hoped that they are different; quantum mechanics never stops surprising me. - Nora Tischler, Farzad Ghafari, Travis J. Baker, Sergei Slussarenko, Raj B. Patel, Morgan M. Weston, Sabine Wollmann, Lynden K. Shalm, Varun B. Verma, Sae Woo Nam, H. Chau Nguyen, Howard M. Wiseman, and Geoff J. Pryde,
*"Conclusive Experimental Demonstration of One-Way Einstein-Podolsky-Rosen Steering"*, Phys. Rev. Lett.**121**100401 (2018). Since oneway steerable states are fragile, proving the oneway steering phenomenon is challenging. In this work, we show that existing experiments demonstrating one-way steering are inconclusive, and carry out the first conclusive experiment realising the phenomenon. - H. Chau Nguyen, Antony Milne, Thanh Vu and Sania Jevtic,
*"Quantum steering with positive operator valued measures"*, J. Phys. A**51**355302 (2018). After quite some time tried and failed, I find very relieved that we are finally able to construct a general approach to study quantum steering with POVMs. As the first application, we use it to show a numerical evidence that POVMs and PVMs are actually equivalent in steering Werner states and T-states (see also IQI open quantum problems). Don't be disappointed; I hope that they are not equivalent in other situations! - H. Chau Nguyen and Kimmo Luoma,
*"On the pure state outcomes of Einstein-Podolsky-Rosen steering"*, Phys. Rev. A**95**042117 (2017). Using the purification technique, we show that pure steering outcomes often carry interesting information about the shared state. As an application, we generalise the fundamental lemma in the so-called `all-versus-nothing proof of steerability' for systems of arbitrary dimension. - H. Chau Nguyen and Thanh Vu,
*"Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes"*, Europhys. Lett.**115**10003 (2016). We derive a necessary and sufficient condition for steerability of two-qubit states, and thereby prove a very interesting conjecture on the steerability of the so-called two-qubit T-states. - H. Chau Nguyen and Thanh Vu,
*"Non-separability and steerability of two-qubit states from the geometry of steering outcomes"*, Phys. Rev. A**94**012114 (2016). We show that the problem of classification of two-qubit states into nonseparable and steerable classes can be understood as a geometrical problem of classifying the so-called double-cones of steering outcomes in the 4D Euclidean space.

*Quantum Physics and Gravity*

- H. Chau Nguyen and Fabian Bernards,
*"Entanglement dynamics of two mesoscopic objects with gravitational interaction"*, arXiv:1906.11184 (2019). Excited by a possible realisation of a simple experiment, which can eventually be considered to some extent as a quantum signature of gravity (modulo some debate), we set out to analyse the exact condition for the experiment to be realisable and how to optimise it. The good news is that the condition turns out to be not very stringent, and we can hope that such an experiment can indeed be realised in the near furture. Theoretically, it is a simple problem, but very fun, and exactly solvable!

*Condensed Matter Physics and Simulated Systems*

- Dung Xuan Nguyen, Xavier Letartre, Emmanuel Drouard, Pierre Vicktorovitch, H. Chau Nguyen, and Hai Son Nguyen,
*"Flatbands and the localisation in moiré superlattice of bilayer phtonic crystal,"*, arXiv:2104.12774 (2021) . We show that a highly flatband can be obtained in photonic crystal in a system and in a manner that is much simpler than that of twisted graphene. The observed flatband is a ornament of a topological effect involved, which we will soon discuss in a next work. - H. Chau Nguyen, Nhung T. T. Nguyen and V. Lien Nguyen,
*"On the density of states of circular graphene quantum dots"*, J. Phys.: Condens. Matter 29 405301 (2017). We suggest a simple, fast and easy method to calculate the LDOS of graphene quantum dots, which avoid the computation by indirectly by the scattering coefficient method and by the finite difference method. - H. Chau Nguyen, Nhung T. T. Nguyen and V. Lien Nguyen,
*"The transfer matrix approach to circular graphene quantum dots"*, J. Phys.: Condens. Matter**28**275301 (2016). This work unifies the calculations of bound states, quasi-bound states and scattering cross-sections of a circular graphene quantum dot in a single framework. - Markus Müller and H. Chau Nguyen,
*"Collision-dominated spin transport in graphene and Fermi liquids"*, New J. Phys.**13**035009 (2011) . The collision-dominated spin transport in graphene and Fermi liquids is studied. An exact relation of spin conductance of pristine graphene with its electronic conductance is established. - C. Huy Pham, H. Chau Nguyen, V. Lien Nguyen,
*"Massless Dirac fermions in a graphene superlattice: a T-matrix approach"*, J. Phys.: Condens. Matter**22**425501 (2010) . Peculiar properties of Dirac fermions in superlattice are derived in a simple manner. - H. Chau Nguyen and V. Lien Nguyen,
*"Tunneling of Dirac electrons through one-dimensional potentials in graphene: a T-matrix approach"*, J. Phys.: Condens. Matter**21**045305 (2009) . A simple method to calculate the conductance of an arbitrary one-dimensional conjunction potential in graphene is formulated. - H. Chau Nguyen, M.Tien Hoang and V. Lien Nguyen,
*"Quasi-bound states induced by one-dimensional potentials in graphene"*, Phys. Rev. B**79**035411 (2009). Here the problem of finding quasi-bound states is made an easy exercise by the transfer matrix method.

*Statistical Inference, Information and Data Science*

- H. Chau Nguyen, Riccardo Zecchina and Johannes Berg
*"Inverse statistical problems: from the inverse Ising problem to data science"*, Advances in Physics (2017). We review some applications and theoretical understanding of the inverse Ising problem. The connection between maximum likelihood inference and thermodynamics is emphasised. Methods of inference in the low sampling regime (pseudolikelihood, interaction screening) are also discussed. - Simon L. Dettmer, H. Chau Nguyen and Johannes Berg,
*"Network inference in the non-equilibrium steady state"*, Phys. Rev. E**94**, 052116 (2016). We show that it is possible (!) to reconstruct the parameters of the dynamical Ising model based on sampled data of the (nonequilibrium) stationary state. - H. Chau Nguyen in Seidel
*et. al.*,*"A genomics-based classification of human lung tumors"*, Science Transl. Med.**5**(29) 209ra153 (2013). We devise a very simple semi-supervised classification method and apply the method to the classification of lung cancers. - H. Chau Nguyen and Johannes Berg,
*"Mean-field theory for the inverse Ising problem at low temperatures"*, Phys. Rev. Lett.**109**050602 (2012). Here the mystery of the failure of mean-field methods for the inverse Ising problem is explained. - H. Chau Nguyen and Johannes Berg,
*"Bethe-Peierls approximation and the inverse Ising problem"*, J. Stat. Mech. P03004 (2012). It is shown that Bethe-Peierls approximation allows for a simple solution to the inverse Ising problem, which is exact in tree.

#### Translations

- Carlo Rovelli,
*The order of time*(Penguin Books) into*Trật tự thời gian*(Vietnamese), published at Omegaplus.

#### Teaching

- SS 2021: Übungen Statistischer Physik
- WS 2020: Introduction to Theoretical Condensed Matter Physics
- WS 2019: Exercises for Quantum Theory of Light
- SS 2019: Quantum Entropy and its Applications
- WS 2018: Exercises for Theory of Quantum Matter
- SS 2018: Exercises for Quantum Information Theory
- WS 2014: Exercises for Statistische Physik
- WS 2013: Exercises for Advanced Statistical Physics
- WS 2012: Exercises for Statistical Physics and Information Theory

#### Current schools and conferences

- Unfortunately the Summer School of Quantum Physics 2020 in Quynhon (Vietnam) has been cancelled due to the complication of the corona virus.

#### Theses

#### Other stuffs

*PS: I truely love textbooks as well as popular physics books and intend to maintain a collection of reviews of textbooks; but this is really in future to come...*