Quantum teleportation with partially entangled states via noisy channels

Using a partially entangled EPR-type state as quantum channel, we investigate quantum teleportation (QT) of a qubit state in noisy environments by solving the master equation in the Lindblad form. We analyze the different influence for the partially entangled EPR-type channel and the EPR channel on the fidelity and the average fidelity of the QT process in the presence of Pauli noises. It is found that the fidelity depends on the type and the strength of the noise, and the initial state to be teleported. Moreover, the EPR channel is more robust than the partially entangled EPR-type channel against the influence of the noises. It is also found that the partially entangled EPR-type channel enables the average fidelity as a function of the decoherence parameter $kt$ to decay with different velocities for different Pauli noises.     

Minimum assured fidelity and minimum average fidelity in quantum teleportation of single qubit using non-maximally entangled states

We study use of non-maximally entangled states (NME) in quantum teleportation (QT) of single qubit. We find that if NME states are written in the form ${| E \rangle =\sum_{j,k} {E_{jk} | j \rangle | k \rangle}}$ , where (j, k) = 0 and 1, and maximally entangled Bell-basis is used in measurement by the sender, the ??Minimum Assured Fidelity?? (the minimum value of fidelity for all possible information states) for QT is 2C/(1?+?C), where C is the concurrence of ${| E \rangle }$ given by C?=?2|det (E)| and E is the matrix defined by the coefficients E _jk . We also find the average of fidelity over various results of Bell-state measurement and its minimum value over all possible information states and discuss it for some special cases. We also show that, to evaluate quality of imperfect QT, minimum assured fidelity is a better measure than concurrence or minimum average fidelity.     

Probabilistic teleportation via multi-parameter measurements and partially entangled states

In this paper, a novel scheme for probabilistic teleportation is presented with multi-parameter measurements via a non-maximally entangled state. This is in contrast to the fact that the measurement kinds for quantum teleportation are usually particular in most previous schemes. The detail implementation producers for our proposal are given by using of appropriate local unitary operations. Moreover, the total success probability and classical information of this proposal are calculated. It is demonstrated that the success probability and classical cost would be changed with the multi-measurement parameters and the entanglement factor of quantum channel. Our scheme could enlarge the research range of probabilistic teleportation.     

Geometric discord and measurement-induced nonlocality for well known bound entangled states

We employ geometric discord and measurement induced nonlocality to quantify quantumness of some well-known bipartite bound entangled states, namely the two families of Horodecki’s ( $2\otimes 4, 3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett et al.’s in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti et al. and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.     

Teleporting an unknown quantum state with unit fidelity and unit probability via a non-maximally entangled channel and an auxiliary system

Quantum Information Processing - We present a new scheme for quantum teleportation that one can teleport an unknown state via a non-maximally entangled channel with certainly, using an auxiliary...     

SLOCC orbit of rank-deficient two-qubit states: quantum entanglement,quantum discord and EPR steering

We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rank-deficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein–Podolsky–Rosen steering ellipsoids corresponding to these states.     

Negativity fonts, multiqubit invariants and four qubit maximally entangled states

Recently, we introduced negativity fonts as the basic units of multipartite entanglement in pure states. We show that the relation between global negativity of partial transpose of N?qubit state and linear entropy of reduced single qubit state yields an expression for global negativity in terms of determinants of negativity fonts. Transformation equations for determinants of negativity fonts under local unitaries (LU??s) are useful to construct LU invariants such as degree four and degree six invariants for four qubit states. The difference of squared negativity and N?tangle is an N qubit invariant which contains information on entanglement of the state caused by quantum coherences that are not annihilated by removing a single qubit. Four qubit invariants that detect the entanglement of specific parts in a four qubit state are expressed in terms of three qubit subsystem invariants. Numerical values of invariants bring out distinct features of several four qubit states which have been proposed to be the maximally entangled four qubit states.     

Extremal properties of conditional entropy and quantum discord for XXZ,symmetric quantum states

For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy \(S_{cond}\) as a function of measurement angle \(\theta \in [0,\pi /2]\). Numerical calculations show that the function \(S_{cond}(\theta )\) for X states can have at most one local extremum in the open interval from zero to \(\pi /2\) (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle \(\theta ^*\). Such \(\theta \)-regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval \((0,\pi /2)\). It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.     

Generation of entangled coherent-squeezed states: their entanglement and nonclassical properties

In this paper, after a brief review on the coherent states and squeezed states, we introduce two classes of entangled coherent-squeezed states. Next, in order to generate the introduced entangled states, we present a theoretical scheme based on the resonant atom-field interaction. In the proposed model, a \(\varLambda \)-type three-level atom interacts with a two-mode quantized field in the presence of two strong classical fields. Then, we study the amount of entanglement of the generated entangled states using the concurrence and linear entropy. Moreover, we evaluate a few of their nonclassical properties such as photon statistics, second-order correlation function, and quadrature squeezing and establish their nonclassicality features.     

Relations between entanglement, Bell-inequality violation and teleportation fidelity for the two-qubit X states

Based on the assumption that the receiver Bob can apply any unitary transformation, Horodecki et al. (Phys Lett A 222:21–25, 1996) proved that any mixed two spin-1/2 state which violates the Bell-CHSH inequality is useful for teleportation. Here, we further show that any X state which violates the Bell-CHSH inequality can also be used for nonclassical teleportation even if Bob can only perform the identity or the Pauli rotation operations. Moreover, we showed that the maximal difference between the two average fidelities achievable via Bob’s arbitrary transformations and via the sole identity or the Pauli rotation is 1/9.     

A revisit to stochastic near-optimal controls: The critical case

This paper revisits the stochastic near-optimal control problem considered in Zhou (1998), where the stochastic system is given by a controlled stochastic differential equation with the control variable taking values in a general control space and entering both the drift and diffusion coefficients. A necessary condition of near-optimality is derived using Ekeland’s variational principle, spike variation techniques, and some delicate estimates for the state and the adjoint processes. We improve the error bound of order from “almost” ${\epsilon }^{\frac{1}{3}}$ in Zhou (1998) to “exactly” ${\epsilon }^{\frac{1}{3}}$.     

A revisit to block and recursive least squares for parameter estimation

In this paper, the classical least squares (LS) and recursive least squares (RLS) for parameter estimation have been re-examined in the light of the present day computing capabilities. It has been demonstrated that for linear time-invariant systems, the performance of blockwise least squares (BLS) is always superior to that of RLS. In the context of parameter estimation for dynamic systems, the current computational capability of personal computers are more than adequate for BLS. However, for time-varying systems with abrupt parameter changes, standard blockwise LS may no longer be suitable due to its inefficiency in discarding “old” data. To deal with this limitation, a novel sliding window blockwise least squares approach with automatically adjustable window length triggered by a change detection scheme is proposed. Two types of sliding windows, rectangular and exponential, have been investigated. The performance of the proposed algorithm has been illustrated by comparing with the standard RLS and an exponentially weighted RLS (EWRLS) using two examples. The simulation results have conclusively shown that: (1) BLS has better performance than RLS; (2) the proposed variable-length sliding window blockwise least squares (VLSWBLS) algorithm can outperform RLS with forgetting factors; (3) the scheme has both good tracking ability for abrupt parameter changes and can ensure the high accuracy of parameter estimate at the steady-state; and (4) the computational burden of VLSWBLS is completely manageable with the current computer technology. Even though the idea presented here is straightforward, it has significant implications to virtually all areas of application where RLS schemes are used.     

Quantum discord for two-qubit systems in the Bloch channel: effects of longitudinal and transversal relaxation times

Quantum discord is studied for two-qubit systems with different settings under the influence of the Bloch channel which is characterized by the longitudinal and transversal relaxation times and the environmental temperature. The relaxation of the quantum discord strongly depends on the ratio of the two relaxation times and the environmental temperature. It is found that the ratio of the quantum discord to the total correlation becomes finite or zero asymptotically, depending on the ratio of the relaxation times and the system setting. Furthermore, the optimal setting for sharing the quantum discord is discussed for given environmental temperature and ratio of the relaxation times.     

Biseparability of noisy pseudopure,W and GHZ states using conditional quantum relative Tsallis entropy

We employ the conditional version of sandwiched Tsallis relative entropy to determine \(1:N-1\) separability range in the noisy one-parameter families of pseudopure and Werner-like N-qubit W, GHZ states. The range of the noisy parameter, for which the conditional sandwiched Tsallis relative entropy is positive, reveals perfect agreement with the necessary and sufficient criteria for separability in the \(1:N-1\) partition of these one parameter noisy states.     

A revisit to the gain and phase margins of linear quadraticregulators

In this paper, we revisit the well-known robustness properties of the linear quadratic regulator (LQR), namely, the guaranteed gain margin of -6 to +∞ dB and phase margin of -60° to +60° for single-input systems. We caution that these guaranteed margins need to be carefully interpreted. More specifically, we show via examples that an LQR may have a very small margin with respect to the variations of the gain and/or phase of the open-loop plant. Such a situation occurs in most practical systems, where the set of measurable state variables cannot be arbitrarily selected. Therefore the lack of robustness of the LQR can be very popular and deserves attention     

A revisit to the common mean problem: Comparing the maximum likelihood estimator with the Graybill-Deal estimator

For estimating the common mean of two normal populations with unknown and possibly unequal variances the well-known Graybill-Deal estimator (GDE) has been a motivating factor for research over the last five decades. Surprisingly the literature does not have much to show when it comes to the maximum likelihood estimator (MLE) and its properties compared to those of the GDE. The purpose of this note is to shed some light on the structure of the MLE, and compare it with the GDE. While studying the asymptotic variance of the GDE, we provide an upgraded set of bounds for its variance. A massive simulation study has been carried out with very high level of accuracy to compare the variances of the above two estimators results of which are quite interesting.     

3D noisy discrete objects: Segmentation and application to smoothing

We propose in this paper a segmentation process that can deal with noisy discrete objects. A flexible approach considering arithmetic discrete planes with a variable width is used to avoid the over-segmentation that might happen when classical segmentation algorithms based on regular discrete planes are used to decompose the surface of the object. A method to choose a seed and different segmentation strategies according to the shape of the surface is also proposed, as well as an application to smooth the border of convex noisy discrete objects.     

A multi-objective optimization problem in mixed and natural convection for a vertical channel asymmetrically heated

Structural and Multidisciplinary Optimization - This paper deals with a multi-objective topology optimization problem in an asymmetrically heated channel, based on both pressure drop minimization...     

Observability analysis of rotation estimation by fusing inertial and line-based visual information: A revisit

This note presents a simple approach to the observability analysis of the rotation estimation using line-based dynamic vision and inertial sensors. The problem was originally raised and formulated in Rehbinder, and Ghosh [2003. Pose estimation using line-based dynamic vision and inertial sensors. IEEE Transactions on Automatic Control, 48(2), 186-199.] where the unobservable subgroup was derived using complex matrix manipulations. By solving linear quaternion equations and using set operations, we not only successfully obtain the same result but also naturally extend it for the case with linearly dependent lines. The development in this note is more straightforward and gives rise to a clearer picture of the problem.     

Extensions of the witness method to characterize under-, over- and well-constrained geometric constraint systems

This paper describes new ways to tackle several important problems encountered in geometric constraint solving, in the context of CAD, and which are linked to the handling of under- and over-constrained systems. It presents a powerful decomposition algorithm of such systems.Our methods are based on the witness principle whose theoretical background is recalled in a first step. A method to generate a witness is then explained. We show that having a witness can be used to incrementally detect over-constrainedness and thus to compute a well-constrained boundary system. An algorithm is introduced to check if anchoring a given subset of the coordinates brings the number of solutions to a finite number.An algorithm to efficiently identify all maximal well-constrained parts of a geometric constraint system is described. This allows us to design a powerful algorithm of decomposition, called W-decomposition, which is able to identify all well-constrained subsystems: it manages to decompose systems which were not decomposable by classic combinatorial methods.