12,316 research outputs found
All-versus-nothing violation of local realism in the one-dimensional Ising model
We show all-versus-nothing proofs of Bell's theorem in the one-dimensional
transverse-field Ising model, which is one of the most important exactly
solvable models in the field of condensed matter physics. Since this model can
be simulated with nuclear magnetic resonance, our work might lead to a fresh
approach to experimental test of the Greenberger-Horne-Zeilinger contradiction
between local realism and quantum mechanics.Comment: 4 page
Tight Correlation-Function Bell Inequality for Multipartite -Dimensional System
We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to multipartite d-dimensional systems. All the Bell
inequalities based on this generalization take the same simple form as the CHSH
inequality. For small systems, numerical results show that the new inequalities
are tight and we believe this is also valid for higher dimensional systems.
Moreover, the new inequalities are relevant to the previous ones and for
bipartite system, our inequality is equivalent to the
Collins-Gisin-Linden-Masser-Popescu (CGLMP) inequality.Comment: 4 pages; Accepted by PR
Machine Learning Bell Nonlocality in Quantum Many-body Systems
Machine learning, the core of artificial intelligence and big data science,
is one of today's most rapidly growing interdisciplinary fields. Recently, its
tools and techniques have been adopted to tackle intricate quantum many-body
problems. In this work, we introduce machine learning techniques to the
detection of quantum nonlocality in many-body systems, with a focus on the
restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning,
we demonstrate that RBM is capable of finding the maximum quantum violations of
multipartite Bell inequalities with given measurement settings. Our results
build a novel bridge between computer-science-based machine learning and
quantum many-body nonlocality, which will benefit future studies in both areas.Comment: Main Text: 7 pages, 3 figures. Supplementary Material: 2 pages, 3
figure
Quantum state complexity and the thermodynamic arrow of time
Why time is a one-way corridor? What's the origin of the arrow of time? We
attribute the thermodynamic arrow of time as the direction of increasing
quantum state complexity. Inspired by the work of Nielsen, Susskind and
Micadei, we checked this hypothesis on both a simple two qubit and a three
qubit quantum system. The result shows that in the two qubit system, the
thermodynamic arrow of time always points in the direction of increasing
quantum state complexity. For the three qubit system, the heat flow pattern
among subsystems is closely correlated with the quantum state complexity of the
subsystems. We propose that besides its impact on macroscopic spatial geometry,
quantum state complexity might also generate the thermodynamic arrow of time.Comment: 4 pages, 4 figure
Distance formulas capable of unifying Euclidian space and probability space
For pattern recognition like image recognition, it has become clear that each
machine-learning dictionary data actually became data in probability space
belonging to Euclidean space. However, the distances in the Euclidean space and
the distances in the probability space are separated and ununified when machine
learning is introduced in the pattern recognition. There is still a problem
that it is impossible to directly calculate an accurate matching relation
between the sampling data of the read image and the learned dictionary data. In
this research, we focused on the reason why the distance is changed and the
extent of change when passing through the probability space from the original
Euclidean distance among data belonging to multiple probability spaces
containing Euclidean space. By finding the reason of the cause of the distance
error and finding the formula expressing the error quantitatively, a possible
distance formula to unify Euclidean space and probability space is found. Based
on the results of this research, the relationship between machine-learning
dictionary data and sampling data was clearly understood for pattern
recognition. As a result, the calculation of collation among data and
machine-learning to compete mutually between data are cleared, and complicated
calculations became unnecessary. Finally, using actual pattern recognition
data, experimental demonstration of a possible distance formula to unify
Euclidean space and probability space discovered by this research was carried
out, and the effectiveness of the result was confirmed
Understanding over-parameterized deep networks by geometrization
A complete understanding of the widely used over-parameterized deep networks
is a key step for AI. In this work we try to give a geometric picture of
over-parameterized deep networks using our geometrization scheme. We show that
the Riemannian geometry of network complexity plays a key role in understanding
the basic properties of over-parameterizaed deep networks, including the
generalization, convergence and parameter sensitivity. We also point out deep
networks share lots of similarities with quantum computation systems. This can
be regarded as a strong support of our proposal that geometrization is not only
the bible for physics, it is also the key idea to understand deep learning
systems.Comment: 6 page
Quantifying Nonlocality Based on Local Hidden Variable Models
We introduce a fresh scheme based on the local hidden variable models to
quantify nonlocality for arbitrarily high-dimensional quantum systems. Our
scheme explores the minimal amount of white noise that must be added to the
system in order to make the system local and realistic. Moreover, the scheme
has a clear geometric significance and is numerically computable due to
powerful computational and theoretical methods for the class of convex
optimization problems known as semidefinite programs.Comment: 4page
Three-dimensional lattice Boltzmann models for solid-liquid phase change
A three-dimensional (3 D) multiple-relaxation-time (MRT) and a 3 D
single-relaxation-time (SRT) lattice Boltzmann (LB) models are proposed for the
solid-liquid phase change. The enthalpy conservation equation can be recovered
from the present models. The reasonable relationship of the relaxation times in
the MRT model is discussed. Both One-dimensional (1 D) melting and
solidification with analytical solutions are respectively calculated by the SRT
and MRT models for validation. Compared with the SRT model, the MRT one is more
accurate to capture the phase interface. The MRT model is also verified with
other published two-dimensional (2 D) numerical results. The validations
suggest that the present MRT approach is qualified to simulate the 3 D
solid-liquid phase change process. Furthermore, the influences of Rayleigh
number and Prandtl number on the 3 D melting are investigated.Comment: 32 pages, 34 figure
SO(4) symmetry in the relativistic hydrogen atom
We show that the relativistic hydrogen atom possesses an SO(4) symmetry by
introducing a kind of pseudo-spin vector operator. The same SO(4) symmetry is
still preserved in the relativistic quantum system in presence of an U(1)
monopolar vector potential as well as a nonabelian vector potential. Lamb shift
and SO(4) symmetry breaking are also discussed.Comment: 4 pages, 1 figur
Maximal Quantum Violation of the CGLMP Inequality on Its Both Sides
We investigate the maximal violations for both sides of the -dimensional
CGLMP inequality by using the Bell operator method. It turns out that the
maximal violations have a decelerating increase as the dimension increases and
tend to a finite value at infinity. The numerical values are given out up to
for positively maximal violations and for negatively
maximal violations. Counterintuitively, the negatively maximal violations tend
to be a little stronger than the positively maximal violations. Further we show
the states corresponding to these maximal violations and compare them with the
maximally entangled states by utilizing entangled degree defined by von Neumann
entropy. It shows that their entangled degree tends to some nonmaximal value as
the dimension increases.Comment: 14 pages, 2 figures. Accepted for publication in International
Journal of Quantum Informatio
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