Chau Nguyen

Postdoc
Room: B-110
Phone: +49 271 740 3506
chau.nguyen@uni-siegen.dePreprints
See also arxiv
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)