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# Chau Nguyen

Postdoc

Room: B-102

Phone: +49 271 740 3506

## Preprints

H. Chau Nguyen and Otfried Gühne
Quantum steering of Bell-diagonal states with generalized measurements
arXiv:1909.03963

The phenomenon of quantum steering in bipartite quantum systems can be reduced to the question whether or not the first party can perform measurements such that the conditional states on the second party can be explained by a local hidden state model. Clearly, the answer to this depends on the measurements which the first party is able to perform. We introduce a local hidden state model explaining the conditional states for all generalized measurements on Bell-diagonal states of two qubits. More precisely, it is known for the restricted case of projective measurements and Bell-diagonal states characterised by the correlation matrix $T$ that a local hidden state model exists if and only if $R_T= 2 \pi N_T |\det (T)| \ge 1$, where $N_T$ is defined by an integral over the Bloch sphere. For generalized measurements described by positive operator valued measures we construct a model if $R_T \ge 6/5$. Our work paves the way for a systematic study of steerability of quantum states with generalized measurements beyond the highly-symmetric Werner states.

H. Chau Nguyen and Fabian Bernards
Entanglement dynamics of two mesoscopic objects with gravitational interaction
arXiv:1906.11184

We analyse the entanglement dynamics of the two particles interacting through gravity in the recently proposed experiments aiming at testing quantum signatures for gravity [Phy. Rev. Lett 119, 240401 & 240402 (2017)]. We consider the open dynamics of the system under decoherence due to the environmental interaction. We show that as long as the coupling between the particles is strong, the system does indeed develop entanglement, confirming the qualitative analysis in the original proposals. We show that the entanglement is also robust against stochastic fluctuations in setting up the system. The optimal interaction duration for the experiment is computed. A condition under which one can prove the entanglement in a device-independent manner is also derived.

Roope Uola, Ana C. S. Costa, H. Chau Nguyen and Otfried Gühne
Quantum Steering
arXiv:1903.06663

Quantum steering is a notion introduced by Schr\"odinger in order to capture the essence of the Einstein-Podolsky-Rosen argument. In this paper we review the theory of quantum steering. We present the basic definitions of steering and local hidden state models and their relation to entanglement and Bell nonlocality. Then, we describe the various criteria to characterize steerability and structural results on the phenomenon. A detailed discussion is given on the connections between steering and incompatibility of quantum measurements. Finally, we review applications of steering in quantum information processing and further related topics.

H. Chau Nguyen, Antony Milne, Thanh Vu and Sania Jevtic
Quantum steering with positive operator valued measures
arXiv:1706.08166

We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of determining the steerability of a bipartite quantum state of finite dimension with POVMs can be formulated as a nesting problem of two convex objects. One consequence of this is the strengthening of the theorem that justifies choosing the LHS ensemble based on symmetry of the bipartite state. As a more practical application, we study the classic problem of the steerability of two-qubit Werner states with POVMs. We show strong numerical evidence that these states are unsteerable with POVMs up to a mixing probability of $\frac{1}{2}$ within an accuracy of $10^{-3}$.

## Publications

H. Chau Nguyen, Huy-Viet Nguyen and Otfried Gühne
The geometry of the Einstein--Podolsky--Rosen correlations
Phys. Rev. Lett. 122, 240401 (2019), arXiv:1808.09349

Correlations between distant particles are central to many puzzles and paradoxes of quantum mechanics and, at the same time, underpin various applications like quantum cryptography and metrology. Originally in 1935, Einstein, Podolsky and Rosen (EPR) used these correlations to argue against the completeness of quantum mechanics. To formalise their argument, Schr\"odinger subsequently introduced the notion of quantum steering. Still, the question which quantum states can be used for the EPR argument and which not remained open. Here we show that quantum steering can be viewed as an inclusion problem in convex geometry. For the case of two spin-$\frac{1}{2}$ particles, this approach completely characterises the set of states leading to the EPR argument and consequently to a full description of the quantum correlations that can be used for steering. Our results find applications in various protocols in quantum information processing, and moreover they are linked to quantum mechanical phenomena such as uncertainty relations and the question which observables in quantum mechanics are jointly measurable.

H. Chau Nguyen, Nhung T. T. Nguyen and V. Lien Nguyen
On the density of states of circular graphene quantum dots
J. Phys.: Cond. Mat. 29, 405301 (2017), arXiv:1705.01035

We suggest a simple approach to calculate the local density of states that effectively applies to any structure created by an axially symmetric potential on a continuous graphene sheet such as circular graphene quantum dots or rings. Calculations performed for the graphene quantum dot studied in a recent scanning tunneling microscopy measurement [{\sl Gutierrez et al. Nat. Phys. \textbf{12}, 1069--1075 (2016)}] show an excellent experimental-theoretical agreement.

H. Chau Nguyen, Riccardo Zecchina and Johannes Berg
Inverse statistical problems: from the inverse Ising problem to data science
Advances in Physics 66 (3), 197-261 (2017), arXiv:1702.01522

Inverse problems in statistical physics are motivated by the challenges of big data' in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetisations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.

H. Chau Nguyen and Kimmo Luoma
On the pure state outcomes of Einstein-Podolsky-Rosen steering
Phys. Rev. A 95, 042117 (2017), arXiv:1612.07607

In the Einstein--Podolsky--Rosen experiment, when Alice makes a measurement on her part of a bipartite system, Bob's part is collapsed to, or steered to, a specific ensemble. Moreover, by reading her measurement outcome, Alice can specify which state in the ensemble Bob's system is steered to and with which probability. The possible states that Alice can steer Bob's system to are called steered states. In this work, we study the subset of steered states which are pure after normalisation. We illustrate that these pure steered states, if they exist, often carry interesting information about the shared bipartite state. This information content becomes particularly clear when we study the purification of the shared state. Some applications are discussed. These include a generalisation of the fundamental lemma in the so-called all-versus-nothing proof of steerability' for systems of arbitrary dimension.

Simon L. Dettmer, H. Chau Nguyen and Johannes Berg
Network inference in the non-equilibrium steady state
Phys. Rev. E 94, 052116 (2016), arXiv:1607.07715

Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks detailed balance. Such non-equilibrium systems occur naturally in applications like neural networks or gene regulatory networks. Here, we focus on the paradigmatic asymmetric Ising model and show that we can learn its parameters from independent samples of the non-equilibrium steady state. We present both an exact inference algorithm and a computationally more efficient, approximate algorithm for weak interactions based on a systematic expansion around mean-field theory. Obtaining expressions for magnetisations, two- and three-point spin correlations, we establish that these observables are sufficient to infer the model parameters. Further, we discuss the symmetries characterising the different orders of the expansion around the mean field and show how different types of dynamics can be distinguished on the basis of samples from the non-equilibrium steady state.

H. Chau Nguyen and Thanh Vu
Necessary and sufficient condition for steerability of two-qubit states by the geometry of steering outcomes
Europhysics Letters 115, 10003 (2016), arXiv:1604.03815

Fully characterizing the steerability of a quantum state of a bipartite system has remained an open problem since the concept of steerability was defined. In this work, using our recent geometrical approach to steerability, we suggest a necessary and sufficient condition for a two-qubit state to be steerable with respect to projective measurements. To this end, we define the critical radius of local models and show that a state of two qubits is steerable with respect to projective measurements from Alice's side if and only if her critical radius of local models is less than $1$. As an example, we calculate the critical radius of local models for the so-called T-states by proving the optimality of a recently-suggested ansatz for Alice's local hidden state model.

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), arXiv:1604.00265

When two qubits A and B are in an appropriate state, Alice can remotely steer Bob's system B into different ensembles by making different measurements on A. This famous phenomenon is known as quantum steering, or Einstein-Podolsky-Rosen steering. Importantly, quantum steering establishes the correspondence not only between a measurement on A (made by Alice) and an ensemble of B (owned by Bob) but also between each of Alice's measurement outcomes and an unnormalized conditional state of Bob's system. The unnormalized conditional states of B corresponding to all possible measurement outcomes of Alice are called Alice's steering outcomes. We show that, surprisingly, the $4$-dimensional geometry of Alice's steering outcomes completely determines both the non-separability of the two-qubit state and its steerability from her side. Consequently, the problem of classifying two-qubit states into non-separable and steerable classes is equivalent to geometrically classifying certain $4$-dimensional skewed double-cones.

H. Chau Nguyen, Nhung T. T. Nguyen and V. Lien Nguyen
The transfer matrix approach to circular graphene quantum dots
J. Phys.: Cond. Mat. 28, 275301 (2016), arXiv:1511.00535

We adapt the transfer matrix ($\T$-matrix) method originally designed for one-dimensional quantum mechanical problems to solve the circularly symmetric two-dimensional problem of graphene quantum dots. In similarity to one-dimensional problems, we show that the generalized $\T$-matrix contains rich information about the physical properties of these quantum dots. In particular, it is shown that the spectral equations for bound states as well as quasi-bound states of a circular graphene quantum dot and related quantities such as the local density of states and the scattering coefficients are all expressed exactly in terms of the $\T$-matrix for the radial confinement potential. As an example, we use the developed formalism to analyse physical aspects of a graphene quantum dot induced by a trapezoidal radial potential. Among the obtained results, it is in particular suggested that the thermal fluctuations and electrostatic disorders may appear as an obstacle to controlling the valley polarization of Dirac electrons.

H. Chau Nguyen in Seidel et. al.
A genomics-based classification of human lung tumors
Science Transl. Med. 5, (29) 209ra153 (2013)

H. Chau Nguyen and Johannes Berg
Mean-field theory for the inverse Ising problem at low temperatures
Phys. Rev. Lett. 109, 050602 (2012), arXiv:1204.5375

The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of spin configurations sampled from the Boltzmann measure. To invert the relationship between model parameters and observables (magnetisations and correlations) mean-field approximations are often used, allowing to determine model parameters from data. However, all known mean-field methods fail at low temperatures with the emergence of multiple thermodynamic states. Here we show how clustering spin configurations can approximate these thermodynamic states, and how mean-field methods applied to thermodynamic states allow an efficient reconstruction of Ising models also at low temperatures.

H. Chau Nguyen and Johannes Berg
Bethe-Peierls approximation and the inverse Ising model
J. Stat. Mech. , P03004 (2012), arXiv:1112.3501

We apply the Bethe-Peierls approximation to the problem of the inverse Ising model and show how the linear response relation leads to a simple method to reconstruct couplings and fields of the Ising model. This reconstruction is exact on tree graphs, yet its computational expense is comparable to other mean-field methods. We compare the performance of this method to the independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations, the Sessak-Monasson expansion, and susceptibility propagation in the Cayley tree, SK-model and random graph with fixed connectivity. At low temperatures, Bethe reconstruction outperforms all these methods, while at high temperatures it is comparable to the best method available so far (Sessak-Monasson). The relationship between Bethe reconstruction and other mean- field methods is discussed.

Markus Müller and H. Chau Nguyen
Collision-dominated spin transport in graphene and Fermi liquids
New J. Phys. 13, 035009 (2011)

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)

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)