A characterization of positive linear maps and criteria of entanglement for quantum states

Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a characterization of positive elementary operators including all positive linear maps between matrix algebras. This characterization is then applied give a representation of quantum channels (operations) between infinite-dimensional systems. A necessary and sufficient criterion of separability is give which shows that a state $\rho$ on $H\otimes K$ is separable if and only if $(\Phi\otimes I)\rho\geq 0$ for all positive finite rank elementary operators $\Phi$. Examples of NCP and indecomposable positive linear maps are given and are used to recognize some entangled states that cannot be recognized by the PPT criterion and the realignment criterion.Comment: 20 page

An Updated Numerical Analysis of eV Seesaw with Four Generations

We consider the so-called "eV seesaw" scenario, with right-handed Majorana mass $M_R$ at eV order, extended to four lepton generations. The fourth generation gives a heavy pseudo-Dirac neutral lepton, which largely decouples from other generations and is relatively stable. The framework naturally gives 3 active and 3 sterile neutrinos. We update a previous numerical analysis of a 3+3 study of the LSND anomaly, taking into account the more recent results from the MiniBooNE experiment. In particular, we study the implications for the third mixing angle $\mathrm{sin}^2\theta_{13}$, as well as CP violation. We find that current data do not seriously constrain more than one sterile neutrinos.Comment: References updated, and a Note Adde

Suppressing decoherence and improving entanglement by quantum-jump-based feedback control in two-level systems

We study the quantum-jump-based feedback control on the entanglement shared between two qubits with one of them subject to decoherence, while the other qubit is under the control. This situation is very relevant to a quantum system consisting of nuclear and electron spins in solid states. The possibility to prolong the coherence time of the dissipative qubit is also explored. Numerical simulations show that the quantum-jump-based feedback control can improve the entanglement between the qubits and prolong the coherence time for the qubit subject directly to decoherence

The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group

In this paper, we give the general forms of the minimal $L$ matrix (the elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal representation of the $A_{n-1}$ series elliptic quantum group given by Felder and Varchenko. The explicit dependence of elements of $L$-matrices on spectral parameter $z$ are given. They are of five different forms (A(1-4) and B). The algebra for the coefficients (which do not depend on $z$) are given. The algebra of form A is proved to be trivial, while that of form B obey Yang-Baxter equation (YBE). We also give the PBW base and the centers for the algebra of form B.Comment: 23 page

Locally fitting hyperplanes to high-dimensional data

Problems such as data compression, pattern recognition and artificial intelligence often deal with a large data sample as observations of an unknown object. An effective method is proposed to fit hyperplanes to data points in each hypercubic subregion of the original data sample. Corresponding to a set of affine linear manifolds, the locally fitted hyperplanes optimally approximate the object in the sense of least squares of their perpendicular distances to the sample points. Its effectiveness and versatility are illustrated through approximation of nonlinear manifolds Möbius strip and Swiss roll, handwritten digit recognition, dimensionality reduction in a cosmological application, inter/extrapolation for a social and economic data set, and prediction of recidivism of criminal defendants. Based on two essential concepts of hyperplane fitting and spatial data segmentation, this general method for unsupervised learning is rigorously derived. The proposed method requires no assumptions on the underlying object and its data sample. Also, it has only two parameters, namely the size of segmenting hypercubes and the number of fitted hyperplanes for user to choose. These make the proposed method considerably accessible when applied to solving various problems in real applications

Entanglement detection beyond the CCNR criterion for infinite-dimensions

In this paper, in terms of the relation between the state and the reduced states of it, we obtain two inequalities which are valid for all separable states in infinite-dimensional bipartite quantum systems. One of them provides an entanglement criterion which is strictly stronger than the computable cross-norm or realignment (CCNR) criterion.Comment: 11 page

Necessary and sufficient conditions for local creation of quantum discord

We show that a local channel cannot create quantum discord (QD) for zero QD states of size $d\geq3$ if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this propertiy is additionally characteristic to the completely decohering channel or the commutativity-preserving unital channel. In particular, the exact forms of the completely decohering channel and the commutativity-preserving unital qubit channel are proposed. Consequently, our results confirm and improve the conjecture proposed by X. Hu et al. for the case of $d\geq3$ and improve the result proposed by A. Streltsov et al. for the qubit case. Furthermore, it is shown that a local channel nullifies QD in any state if and only if it is a completely decohering channel. Based on our results, some protocols of quantum information processing issues associated with QD, especially for the qubit case, would be experimentally accessible.Comment: 8 page

Geodesic scattering by surface deformations of a topological insulator

We consider the classical ballistic dynamics of massless electrons on the conducting surface of a three-dimensional topological insulator, influenced by random variations of the surface height. By solving the geodesic equation and the Boltzmann equation in the limit of shallow deformations, we obtain the scattering cross section and the conductivity {\sigma}, for arbitrary anisotropic dispersion relation. At large surface electron densities n this geodesic scattering mechanism (with {\sigma} propto sqrt{n}) is more effective at limiting the surface conductivity than electrostatic potential scattering.Comment: 9 pages, 5 figure