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 dd-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 $d$-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 $d=10^6$ for positively maximal violations and $d=2\times 10^5$ 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