The relation between Hardy’s non-locality and violation of Bell inequality

We give an analytic quantitative relation between Hardy’s non-locality and Bell operator. We find that Hardy’s non-locality is a sufficient condition for the violation of Bell inequality, the upper bound of Hardy’s non-locality allowed by information causality just corresponds to Tsirelson bound of Bell inequality and the upper bound of Hardy’s non-locality allowed by the principle of no-signaling just corresponds to the algebraic maximum of Bell operator. Then we study the Cabello’s argument of Hardy’s non-locality (a generalization of Hardy’s argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy’s non-locality under the constraint of information causality with the aid of the above derived relation between Hardy’s non-locality and Bell operator.     

Concurrence, tangle and fully entangled fraction

We show that although we cannot distil a singlet from many pairs of bound entangled states, the concurrence and the tangle of two entangled quantum states are always strictly larger than those of one of them, even both entangled quantum states are bound entangled. We present a relation between the concurrence and the fidelity of optimal teleportation. We also give new upper and lower bounds for concurrence and tangle.     

Maximal Violation of Bell Inequality for Any Given Two-Qubit Pure State

In the case of bipartite two-qubit systems, we derive an analytical expression of bound Bell operator for any given pure state. Our result not only manifests some properties of Bell inequality, for example, which may be violated by any pure entangled state and only be maximally violated for a maximally entangled state, but also gives the explicit values of maximal violation for any pure state. Finally we point out that any mixed states which can produce maximal violation of Bell inequality must have a maximal concurrence value.     

Entanglement Dynamics and Bell Violations of Two Atoms in Tavis-Cummings Model with Phase Decoherence

Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.     

Optical scaled Fresnel--Fourier transform obtained via intermediate coordinate-- momentum representation

Using the intermediate coordinate--momentum representation |x>_s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F(r,s) and the Fourier transform operator F by decomposing U. We also find that the matrix element _s,r< x| U|f> just corresponds to an optical scaled Fresnel--Fourier transform.     

Measuring the Wigner Functions of Two-Mode Cavity Fields and Testing the Bell＇s Inequalities

We propose a scheme for measuring the Wigner function of a two-mode cavity field. The scheme bases on the interaction between the two-mode cavity field and three-level atoms. We find a simple relation between the Wigner function and the atomic population. One can obtain the Wigner function by measuring the atomic population with a micromaser-like experiment and doing a numerical integral. By using the two-mode Wigner function one can obtain the Clauser-Horne combination and test the Bell‘s inequalities. We test our equations with a two-mode entanglement state and the results are rather good.     

Numerical Simulation of Bell Inequality's Violation Using Optical Transverse Modes in Multimode Waveguides

We numerically demonstrate that ＇mode-entangled states＇ based on the transverse modes of classical optical fields in multimode waveguides violate Bell＇s inequality. Numerically simulating the correlation measurement scheme of Bell＇s inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell＇s inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.     

Locally Accessible Information from Multipartite Ensembles

We present a universal Holevo-like upper bound on the locally accessible information for arbitrary multipartite ensembles. This bound allows us to analyze the indistinguishability of a set of orthogonal states under local operations and classical communication. We also derive the upper bound for the capacity of distributed dense coding with multipartite senders and multipartite receivers.     

Experimental Demonstration of Deterministic Entanglement Transformation

According to Nielsen＇s theorem [Phys. Rev. Lett. 83 （1999） 436] and as a proof of principle, we demonstrate the deterministic transformation from a maximum entangled state to an arbitrary nonmaximum entangled pure state with local operation and classical communication in an optical system. The output states are verified with a quantum tomography process. We further test the violation of Bell-like inequality to demonstrate the quantum nonlocality of the state we generated. Our results may be useful in quantum information processing.     

A Simple Scheme for Directly Measuring the Wigner Functions of Cavity Fields

We propose a scheme for directly measuring the Wigner functions of cavity fields.The scheme is based on the Raman interaction between atoms and cavity fields.We find a simple and direct relation between the Wigner function and the atomic population difference,By suitablychoosing the interaction time,we find that the wigner function is just two times of the atomic population difference.Thus,one can obtain the Wigner function by measuring the atomic populations and calculating the population difference.     

Non-Classical Correlated Photon Pairs Generation via Cascade Transition of 5S1/2-5P3/2-5D5/2 in a Hot SSRb Atomic Vapor

We experimentally prepare the non-classical correlated photon pairs at the wavelengths of 780 and 776 mn via the cascade transition of 5S1/2 5P3/2-5D5/2 in a hot SSRb atomic ensemble. By measuring the function of cross-correlation and auto-correlation of photons, a violation of Cauehy Schwarz inequality by a factor of 283 is obtained, which clearly indicates a strong non-classicM correlation between the generated photons. We also find that noise photons scattered from pump lasers have a strong effect on the Cauchy-Schwarz inequality factor by changing the intensity of the pump laser, the experimental results are consistent with the theoretical predictions.     

A new class of states of reversible entanglement manipulation under positive partial transpose operations

We first study the reversibility for a class of states under the operations which completely preserve the positivity of partial transpose(PPT) and show that the entanglement cost is equal to the distillable entanglement for a rank-two mixed state on the 4 4 antisymmetric subspace under PPT operations. By using a similar method in finding the irreversibility,we also find that the value of a new efficiently computable additive lower bound Eη(ρ) for the asymptotic PPT-relative entropy of entanglement presented in [Phys. Rev. Lett. 119, 180506(2017)] is equal to the regularized Rains' bound and an upper bound EN(ρ) for distillable entanglement for these states. Furthermore, we find states on the symmetric subspace satisfying the relation mentioned above, generalize the antisymmetric states and symmetric states in higher dimensions, and give a specific value for distillable entanglement and entanglement cost for these states under the PPT operations.     

Uncertainty relation of successive measurements based on Wigner–Yanase skew information

Wigner-Yanase skew information could quantify the quantum uncertainty of the observables that are not commuting with a conserved quantity.We present the uncertainty principle for two successive projective measurements in terms of Wigner-Yanase skew information based on a single quantum system.It could capture the incompatibility of the observables,i.e.the lower bound can be nontrivial for the observables that are incompatible with the state of the quanaim system.Furthermore,the lower bound is also constrained by the quantum Fisher information.In addition,we find the complementarity relation between the uncertainties of the observable which operated on the quantum state and the other observable that performed on the post-measured quantum state and the uncertainties formed by the non-degenerate quantum observables performed on the quantum state,respectively.     

The study of B→K*l+l- decays in family non-universal Z′ models

In a combined investigation of B → K ( * ) l + l - decays, constraints on the related couplings in family non-universal Z′ models are derived. We find that within the allowed parameter space, the recently observed forward-backward asymmetry in the B → K * l + l - decay can be explained by flipping the signs of the Wilson coefficients C eff 9 and C 10 . With the obtained constraints, we also calculate the branching ratio of the B s →μ + μ - decay. The upper bound of our prediction is nearly an order of magnitude smaller than the upper bound given by the CDF Collaboration recently.     

Minimum detection efficiency for the loophole-free confirmation of quantum contextuality

Klyachko–Can–Binicioglu–Shumovsky (KCBS) inequality is a Bell-like inequality,the violation of which can be used to confirm the existence of quantum contextuality.However,the imperfection of detection efficiency may cause the so-called loophole in actual KCBS’s experiments.We derive an alternative KCBS inequality to deal with the loophole in actual KCBS’s experiments.We prove that if the experimental data violate this KCBS inequality,the loophole-free violation of the original KCBS inequality will occur.We show that the minimum detection efficiency needed for a loophole-free violation of the KCBS inequality is about 0.9738.     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Hierarchical Polygamy Inequality for Entanglement of Tsallis q-Entropy

In this paper, we study the polygamy inequality of quantum entanglement in terms of Tsallis q-entropy.We first give a lower bound of Tsallis q-entropy entanglement of assistance(TOA) in the 2  d systems. The relationships between Tsallis q-entropy entanglement(TEE) and TOA are also given. Furthermore, we prove TOA follows a hierarchical polygamy inequality in a 2  2  2~(N-2) systems.     

Separability of Bipartite Superoperator Based on Witnes

Based on the isomorphic relation between operator space L（H） and Hilbert space H^2, Cirac et al. mapped the global superoperator to a mixed state E which has the same separability of the initial superoperator. Zhang et al. [Phys. Rev. A 76 （2007） 012334] provided a calculable lower bound for both the linear and nonlinear witness. We use this bound to detect the entanglement of E to judge the separability of the initial superoperator. With the help of local orthogonal observables, we directly describe the separable condition of superoperator by its each operator. Lastly, using the lower bound of the nonlinear witness, we provide a calculable entanglement factor of bipartite superoperator.     

Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.