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

New Constraint on the Parameters in Cabibbo-Kobayashi-Maskawa Matrix of Wolfenstein's Parametrization

Based on the relation between CP-violation phase and the other three mixing angles in Cabibbo-Kobayashi-Maskawa matrix postulated by us before, a new constraint on the parameters of Wolfenstein's parametrization is given. The result is consistent with the relative experimental results and can be further put to the more precise tests in future.Comment: 5 pages, Latex file, the final revised version for submittin

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

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

Bell Inequality Based on Peres-Horodecki Criterion

We established a physically utilizable Bell inequality based on the Peres-Horodecki criterion. The new quadratic probabilistic Bell inequality naturally provides us a necessary and sufficient way to test all entangled two-qubit or qubit-qutrit states including the Werner states and the maximally entangled mixed states.Comment: 4 pages, 2 figures. Revised version. Title and Figures changed, references adde

Quantum backflow in solutions to the Dirac equation of the spin-1/21/2 free particle

It was known that a free, nonrelativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current --- hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has counterpart in nonrelativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.Comment: 5 pages, 1 figur

On realizing Lov\'asz-optimum orthogonal representation in the real Hilbert space

Quantum contextuality is usually revealed by the non-contextual inequality, which can always be associated with an exclusivity graph. The quantum upper bound of the inequality is nothing but the Lov\'asz number of the graph. In this work, we show that if there is a Lov\'asz-optimum orthogonal representation realized in the $d$-dimensional complex Hilbert space, then there always exists a corresponding Lov\'asz-optimum orthogonal representation in the $(2d-1)$-dimensional real Hilbert space. This in turn completes the proof that the Lov\'asz-optimum orthogonal representation for any exclusivity graph can always be realized in the real Hilbert space of suitable dimension

Bell's Nonlocality Can be Tested through Einstein-Podolsky-Rosen Steering

Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is correspondingly easier to be demonstrated without the detection loophole. In this work, we trigger an extraordinary approach to investigate Bell's nonlocality, which is strongly based on the EPR steering. We present a theorem, showing that for any two-qubit state $\tau$, if its mapped state $\rho$ is EPR steerable, then the state $\tau$ must be Bell nonlocal. The result not only pinpoints a deep connection between EPR steering and Bell's nonlocality, but also sheds a new light to realize a loophole-free Bell-test experiment (without the CHSH inequality) through the violation of steering inequality.Comment: 4 pages, 2 figures. Supplementary Materials, 4 page