Decoherence dynamics of geometric measure of quantum discord and measurement induced nonlocality for noninertial observers at finite temperature

Quantum discord quantifies the total non-classical correlations in mixed states. It is the difference between total correlation, measured by quantum mutual information, and the classical correlation. Another step forward towards the quantification of quantum discord was by Daki? et al. (Phys Rev Lett 105:190502, 2010) who introduced the geometric measure of quantum discord (GMQD) and derived an explicit formula for a two-qubit state. Recently, Luo and Fu (Phys Rev Lett 106:120401, 2011) introduced measurement-induced nonlocality (MIN) as a measure of nonlocality for a bipartite quantum system. The dynamics of GMQD is recently considered by Song et al. (arXiv: quant/ph.1203.3356) and Zhang et al. (Eur Phys J D 66:34, 2012) for inertial observers. However, the topic requires due attention in noninertial frames, particularly, from the perspective of MIN. Here I consider $X$ -structured bipartite quantum system in noninertial frames and analyze the decoherence dynamics of GMQD and MIN at finite temperature. The dynamics under the influence of amplitude damping, depolarizing and phase flip channels is discussed. It is worth-noting that initial state entanglement plays an important role in bipartite states. It is possible to distinguish the Bell, Werner and general type initial quantum states using GMQD. Sudden transition in the behaviour of GMQD and MIN occurs depending upon the mean photon number of the local environment. The transition behaviour disappears for larger values of $\bar{n},$ i.e. $\bar{n}>0.3.$ It becomes more prominent, when environmental noise is introduced in the system. In the presence of environmental noise, as we increase the value of acceleration $r$ , GMQD and MIN decay due to Unruh effect. The effect is prominent for the phase flip and amplitude damping channels. However, in case of depolarizing channel, no sudden change in the behaviour of GMQD and MIN is observed. The environmental noise has stronger affect on the dynamics of GMQD and MIN as compared to the Unruh effect. Furthermore, Werner like states are more robust than General type initial states at finite temperature.     

Geometric measure of quantum discord for a two-parameter class of states in a qubit–qutrit system under various dissipative channels

Quantum discord, as a measure of all quantum correlations, has been proposed as the key resource in certain quantum communication tasks and quantum computational models without containing much entanglement. Daki? et al. (Phys Rev Lett 105:190502, 2010) introduced a geometric measure of quantum discord (GMQD) and derived an explicit formula for any two-qubit state. Luo and Fu (Phys Rev A 82:034302, 2010) introduced another form of GMQD and derived an explicit formula for arbitrary state in a bipartite quantum system. However, the explicit analytical expression for any bipartite system was not given. In this work, we give out the explicit analytical expressions of the GMQD for a two-parameter class of states in a qubit–qutrit system and study its dynamics for the states under various dissipative channels in the first time. Our results show that all these dynamic evolutions do not lead to a sudden vanishing of GMQD. Quantum correlations vanish at an asymptotic time for local or multi-local dephasing, phase-flip, and depolarizing noise channels. However, it does not disappear even though t → ∞ for local trit-flip and local trit-phase-flip channels. Our results maybe provide some important information for the application of GMQD in hybrid qubit–qutrit systems in quantum information.     

Analytic expressions of discord and geometric discord in Werner derivatives

Werner derivatives are a special kind of mixing states transformed from Werner states by unitary operations (Hiroshima and Ishizaka in Phys Rev A 62:044302, 2000). In this paper, the inherent quantum correlations in Werner derivatives are quantified by two different quantifiers, i.e., quantum discord and geometric discord. Different analytic expressions of the two discords in Werner derivatives are derived out. Some distinct features of the discords and their underlying physics are exposed via discussions and analyses. Moreover, it is found that the amount of quantum correlations quantified by either quantifier in each derivative cannot exceed that in the original Werner state. In other words, no unitary operation can increase quantum correlation in a Werner state as far as the two quantifiers are concerned.     

Computing hypergraph Ramsey numbers by using quantum circuit

Gaitan and Clark (Phys Rev Lett 108:010501, 2012) have recently shown a quantum algorithm for the computation of the Ramsey numbers using adiabatic quantum evolution. We present a quantum algorithm to compute the two-color Ramsey numbers for $r$ -uniform hypergraphs by using the quantum counting circuit.     

Flexible protocol for quantum private query based on B92 protocol

Jakobi et al. for the first time proposed a novel and practical quantum private query (QPQ) protocol based on SARG04 (Scarani et al. in Phys Rev Lett 92:057901, 2004) quantum key distribution protocol (Jakobi et al. in Phys Rev A 83:022301, 2011). Gao et al. generalized Jakobi et al’s protocol and proposed a flexible QPQ protocol (Gao et al. in Opt Exp 20(16):17411–17420, 2012). When $\theta <\pi /4$ , Gao et al’s protocol exhibits better database security than Jakobi et al’s protocol, but has a higher probability with which Bob can correctly guess the address of Alice’s query. In this paper, we propose a flexible B92-based QPQ protocol. Although SARG04 protocol is a modification of B92 protocol and can be seen as a generalization of B92 protocol, our protocol shows different advantages from Gao et al’s protocol. It can simultaneously obtain better database security and a lower probability with which Bob can correctly guess the address of Alice’s query when $\theta <\pi /4$ . By introducing entanglement, the proposed QPQ protocol is robust against channel-loss attack, which also implies lower classical communication complexity. Similar to Gao et al’s protocol, it is flexible, practical, and robust against quantum memory attack.     

Limit theorems for decoherent two dimensional quantum walks

In this paper we consider the model with decoherence operators introduced by Brun et?al. (Phys Rev A 67:032304, 2003) which has recently been considered in the two-dimensional setting by Ampadu (Commun Theor Phys, 2011) to obtain the limit of the decoherent quantum walk.     

An alternate quantum adiabatic evolution for the Deutsch–Jozsa problem

Deutsch–Jozsa algorithm has been implemented via quantum adiabatic evolutions by Das et al. (Phys Rev A 65:062310, 2002) and Wei et al. (Phys Lett A 354:271, 2006). In the latter literature, the authors have shown a modified version of the adiabatic evolution which can improve the performance of the algorithm of S. Das et al’s to constant time. In this paper, we also improve the algorithm of S. Das et al’s in a constant time but by using a different construction of adiabatic evolution, i.e., adding ancillary qubits. The algorithm in this paper provides an alternative option to potential users.     

pth Moment Exponential Stability of Stochastic Recurrent Neural Networks with Markovian Switching

This paper investigates the problem of the pth moment exponential stability for a class of stochastic recurrent neural networks with Markovian jump parameters. With the help of Lyapunov function, stochastic analysis technique, generalized Halanay inequality and Hardy inequality, some novel sufficient conditions on the pth moment exponential stability of the considered system are derived. The results obtained in this paper are completely new and complement and improve some of the previously known results (Liao and Mao, Stoch Anal Appl, 14:165–185, 1996; Wan and Sun, Phys Lett A, 343:306–318, 2005; Hu et al., Chao Solitions Fractals, 27:1006–1010, 2006; Sun and Cao, Nonlinear Anal Real, 8:1171–1185, 2007; Huang et al., Inf Sci, 178:2194–2203, 2008; Wang et al., Phys Lett A, 356:346–352, 2006; Peng and Liu, Neural Comput Appl, 20:543–547, 2011). Moreover, a numerical example is also provided to demonstrate the effectiveness and applicability of the theoretical results.     

Hermitian Compact Interpolation on the Cubed-Sphere Grid

The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in Sadourny (Mon Weather Rev 100:136–144, 1972). We extend to this grid the design of high-order finite-difference compact operators (Collatz, The numerical treatment of differential equations. Springer, Berlin, 1960; Lele, J Comput Phys 103:16–42, 1992). The present work is limitated to the design of a fourth-order accurate spherical gradient. The treatment at the interface of the six patches relies on a specific interpolation system which is based on using great circles in an essential way. The main interest of the approach is a fully symmetric treatment of the sphere. We numerically demonstrate the accuracy of the approximate gradient on several test problems, including the cosine-bell test-case of Williamson et al. (J Comput Phys 102:211–224, 1992) and a deformational test-case reported in Nair and Lauritzen (J Comput Phys 229:8868–8887, 2010).     

One sided indeterminism alone is not a useful resource to simulate any nonlocal correlation

Determinism, no signaling and measurement independence are some of the constraints required for framing Bell inequality. Any model simulating nonlocal correlations must either individually or jointly give up these constraints. Recently Hall (Phys Review A, 84:022102, 2011) derived different forms of Bell inequalities under the assumption of individual or joint relaxation of those constraints on both (i.e., two) the sides of a bipartite system. In this work, we have investigated whether one sided relaxation can also be a useful resource for simulating nonlocal correlations or not. We have derived Bell-type inequalities under the assumption of joint relaxation of these constraints only by one party of a bipartite system. Interestingly, we found that any amount of randomness in correlations of one party in absence of signaling between two parties is incapable of showing any sort of Bell–CHSH violation, whereas signaling and measurement dependence individually can simulate any nonlocal correlations. We have also completed the proof of a recent conjecture due to Hall (Phys. Rev. A 82:062117, 2010; Phys. Rev. A 84:022102, 2011) for one-sided relaxation scenario only.     

Maximally discordant separable two-qubit X states

In a recent article, Gharibian (Phys Rev A 86:042106 2012) has conjectured that no two-qubit separable state of rank greater than two could be maximally non-classical (defined to be those which have normalized geometric discord 1/4) and asked for an analytic proof. In this work, we prove analytically that among the subclass of \(X\) states, there is a unique (up to local unitary equivalence) maximal separable state of rank two. For the general case, we derive some necessary conditions.     

Effectiveness of depolarizing noise in causing sudden death of entanglement

Continuing on the recent observation that sudden death of entanglement can occur even when a single qubit of a 2-qubit state is exposed to noisy environment (Yashodamma and Sudha in Results Phys 3:41–45, 2013), we examine the local action of a noise on bipartite qubit–qutrit and qutrit–qutrit systems. We show that depolarizing noise causes sudden death of entanglement in both qubit–qutrit and qutrit–qutrit systems even when it acts only on one part of the system. While generalized amplitude damping noise also causes finite-time disentanglement in qubit–qutrit states, the entanglement sudden death occurs much faster due to depolarizing noise. This result strengthens the observation (Yashodamma and Sudha in Results Phys 3:41–45, 2013) that depolarizing noise is more effective than other noise models in causing sudden death of entanglement.     

Quantum discord of ensemble of quantum states

We highlight an information-theoretic meaning of quantum discord as the gap between the accessible information and the Holevo bound in the framework of ensemble of quantum states. This complementary relationship implies that a large amount of preexisting arguments about the evaluation of quantum discord can be directly applied to the accessible information and vice versa. For an ensemble of two pure qubit states, we show that one can avoid the optimization problem with the help of the Koashi–Winter relation. Further, for the general case (two mixed qubit states), we recover the main results presented by Fuchs and Caves (Phys Rev Lett 73:3047, 1994), but totally from the perspective of quantum discord. Following this line of thought, we also investigate the geometric discord as an indicator of quantumness of ensembles in detail. Finally, we give an example to elucidate the difference between quantum discord and geometric discord with respect to optimal measurement strategies.     

Some types of filters in residuated lattices

In this paper, inspired by some types of $BL$ -algebra filters (deductive systems) introduced in Haveshki et al. (Soft Comput 10:657–664, 2006), Kondo and Dudek (Soft Comput 12:419–423, 2008) and Turunen (Arch Math Log 40:467–473, 2001), we defined residuated lattice versions of them and study them in connection with Van Gasse et al. (Inf Sci 180(16):3006–3020, 2010), Lianzhen and Kaitai (Inf Sci 177:5725–5738, 2007), Zhu and Xu (Inf Sci 180:3614–3632, 2010). Also we consider some relations between these filters and quotient residuated lattice that are constructed via these filters.     

Quantum correlations in a family of bipartite separable qubit states

Quantum correlations (QCs) in some separable states have been proposed as a key resource for certain quantum communication tasks and quantum computational models without entanglement. In this paper, a family of nine-parameter separable states, obtained from arbitrary mixture of two sets of bi-qubit product pure states, is considered. QCs in these separable states are studied analytically or numerically using four QC quantifiers, i.e., measurement-induced disturbance (Luo in Phys Rev A77:022301, 2008), ameliorated MID (Girolami et al. in J Phys A Math Theor 44:352002, 2011),quantum dissonance (DN) (Modi et al. in Phys Rev Lett 104:080501, 2010), and new quantum dissonance (Rulli in Phys Rev A 84:042109, 2011), respectively. First, an inherent symmetry in the concerned separable states is revealed, that is, any nine-parameter separable states concerned in this paper can be transformed to a three-parameter kernel state via some certain local unitary operation. Then, four different QC expressions are concretely derived with the four QC quantifiers. Furthermore, some comparative studies of the QCs are presented, discussed and analyzed, and some distinct features about them are exposed. We find that, in the framework of all the four QC quantifiers, the more mixed the original two pure product states, the bigger QCs the separable states own. Our results reveal some intrinsic features of QCs in separable systems in quantum information.     

Secure multiparty quantum secret sharing with the collective eavesdropping-check character

Combining the block transmission in Long and Liu (Phys Rev A 65:032302, 2002) and the double operations in Lin et al. (Opt Commun 282:4455, 2009), we propose a secure multiparty quantum secret sharing protocol with the collective eavesdropping-check character. In this protocol, only the boss needs to prepare Bell states and perform Bell state measurements, and all agents only perform local operations, which makes this protocol more feasible with the current technique. Incidentally, we show that the other half of secret messages in Lin et al. protocol (Opt Commun 282:4455, 2009) may also be eavesdropped.     

On the modelling of time-interleaved sequential lamination micromixers

We develop a novel and simple theoretical model of time-interleaved sequential lamination micromixers that improves the model proposed by Nguyen and coworkers (Microfluid Nanofluid 1:373–375, 2005a, Lab Chip 5:1320–1326, b, J Phys Conf Ser 34:136–141, 2006) based on the Taylor–Aris dispersion theory. The Nguyen model takes into account the non uniform structure of the velocity profile through an effective dispersion coefficient. However, it is essentially a one-dimensional model that is not suitable to describe (i) neither the behavior of mixing occurring at short length-scales, and characterized by the growth of a mixing boundary layer near the channel walls, (ii) nor the exponential decay of the concentration field occurring at larger length-scales. The model we propose, which is based upon the theory of imaginary potential developed by Giona et?al. (J Fluid Mech 513:221–237, 2004, Europhys Lett 83:34001, 2008, J Fluid Mech 639:291–341, 2009a), is able to provide quantitative predictions on the evolution of the L ²-norm of the concentration fields as function of the axial coordinate ξ,?both for short and asymptotic lengthscales. The quantitative comparison with respect to the Nguyen model is illustrated and discussed. Finally, the coupling between parallel lamination and sequential segmentation is analyzed, and leads to unexpected and apparently counter-intuitive findings.     

A Splitting Algorithm for Image Segmentation on Manifolds Represented by the Grid Based Particle Method

We propose a numerical approach to solve variational problems on manifolds represented by the grid based particle method (GBPM) recently developed in Leung et al. (J. Comput. Phys. 230(7):2540–2561, 2011), Leung and Zhao (J. Comput. Phys. 228:7706–7728, 2009a, J. Comput. Phys. 228:2993–3024, 2009b, Commun. Comput. Phys. 8:758–796, 2010). In particular, we propose a splitting algorithm for image segmentation on manifolds represented by unconnected sampling particles. To develop a fast minimization algorithm, we propose a new splitting method by generalizing the augmented Lagrangian method. To efficiently implement the resulting method, we incorporate with the local polynomial approximations of the manifold in the GBPM. The resulting method is flexible for segmentation on various manifolds including closed or open or even surfaces which are not orientable.     

Weights Design For Maximal Order WENO Schemes

Weighted essentially non-oscillatory (WENO) finite difference schemes, developed by Liu et al. (Comput Phys 115(1):200–212, 1994) and improved by Jiang and Shu (Comput Phys 126(1):202–228, 1996), are one of the most popular methods to approximate the solutions of hyperbolic equations. But these schemes fail to provide maximal order accuracy near smooth extrema, where the first derivative of the solution becomes zero. Some authors have addressed this problem with different weight designs. In this paper we focus on the weights proposed by Yamaleev and Carpenter (J Comput Phys 228:4248–4272, 2009). They propose new weights to provide faster weight convergence than those presented in Borges et al. (J Comput Phys 227:3191–3211, 2008) and deduce some constraints on the weights parameters to guarantee that the WENO scheme has maximal order for sufficiently smooth solutions with an arbitrary number of vanishing derivatives. We analyze the scheme with the weights proposed in Yamaleev and Carpenter (J Comput Phys 228:4248–4272, 2009) and prove that near discontinuities it achieves worse orders than classical WENO schemes. In order to solve these accuracy problems, we define new weights, based on those proposed in Yamaleev and Carpenter (J Comput Phys 228:4248–4272, 2009), and get some constraints on the weights parameters to guarantee maximal order accuracy for the resulting schemes.