Consistent Model and Moment Selection Criteria for GMM Estimation with Applications to Dynamic Panel Data Models

This paper develops consistent model and moment selection criteria for GMM estimation. The criteria select the correct model specification and all correct moment conditions asymptotically. The selection criteria resemble the widely used likelihood-based selection criteria BIC, HQIC, and AIC. (The latter is not consistent.) The GMM selection criteria are based on the J statistic for testing over-identifying restrictions. Bonus terms reward the use of fewer parameters for a given number of moment conditions and the use of more moment conditions for a given number of parameters. The paper applies the model and moment selection criteria to dynamic panel data models with unobserved individual effects. The paper shows how to apply the selection criteria to select the lag length for lagged dependent variables, to detect the number and locations of structural breaks, to determine the exogeneity of regressors, and/or to determine the existence of correlation between some regressors and the individual effect. To illustrate the finite sample performance of the selection criteria and their impact on parameter estimation, the paper reports the results of a Monte Carlo experiment on a dynamic panel data model.Akaike information criterion, Bayesian information criterion, consistent selection procedure, generalized method of moments estimator, instrumental variables estimator, model selection, moment selection, panel data model, test of over-identifying restrictions

Consistent Model and Moment Selection Criteria for GMM Estimation with Application to Dynamic Panel Data Models

This paper develops consistent model and moment selection criteria for GMM estimation. The criteria select the correct model specification and all correct moment conditions asymptotically. The selection criteria resemble the widely used likelihood-based selection criteria BIC, HQIC, and AIC. (The latter is not consistent.) The GMM selection criteria are based on the J statistic for testing over-identifying restrictions. Bonus terms reward the use of fewer parameters for a given number of moment conditions and the use of more moment conditions for a given number of parameters. The paper applies the model and moment selection criteria to dynamic panel data models with unobserved individual effects. The paper shows how to apply the selection criteria to select the lag length for lagged dependent variables, to detect the number and locations of structural breaks, to determine the exogeneity of regressors, and/or to determine the existence of correlation between some regressors and the individual effect. To illustrate the finite sample performance of the selection criteria and their impact on parameter estimation, the paper reports the results of a Monte Carlo experiment on a dynamic panel data model

Entanglement dynamics of three-qubit states in noisy channels

We study entanglement dynamics of the three-qubit system which is initially prepared in pure Greenberger-Horne- Zeilinger (GHZ) or W state and transmitted through one of the Pauli channels $\sigma_z, \, \sigma_x, \, \sigma_y$ or the depolarizing channel. With the help of the lower bound for three-qubit concurrence we show that the W state preserves more entanglement than the GHZ state in transmission through the Pauli channel $\sigma_z$. For the Pauli channels $\sigma_x, \, \sigma_y$ and the depolarizing channel, however, the entanglement of the GHZ state is more resistant against decoherence than the W-type entanglement. We also briefly discuss how the accuracy of the lower bound approximation depends on the rank of the density matrix under consideration.Comment: 2 figures, 32 reference

Quantum computing with mixed states

We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no efficient classical algorithms are known. We suggest a new implementation of quantum computation with initially mixed states in which an algorithm realization is achieved by means of optimal basis independent transformations of qubits.Comment: 2 figures, 52 reference

Rescaling multipartite entanglement measures for mixed states

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.Comment: Published version plus one important reference (Ref. [39]

Quantum Correlation in One-dimensional Extend Quantum Compass Model

We study the correlations in the one-dimensional extended quantum compass model in a transverse magnetic field. By exactly solving the Hamiltonian, we find that the quantum correlation of the ground state of one-dimensional quantum compass model is vanishing. We show that quantum discord can not only locate the quantum critical points, but also discern the orders of phase transitions. Furthermore, entanglement quantified by concurrence is also compared.Comment: 8 pages, 14 figures, to appear in Eur. Phys. J.

State transfer in dissipative and dephasing environments

By diagonalization of a generalized superoperator for solving the master equation, we investigated effects of dissipative and dephasing environments on quantum state transfer, as well as entanglement distribution and creation in spin networks. Our results revealed that under the condition of the same decoherence rate $\gamma$, the detrimental effects of the dissipative environment are more severe than that of the dephasing environment. Beside this, the critical time $t_c$ at which the transfer fidelity and the concurrence attain their maxima arrives at the asymptotic value $t_0=\pi/2\lambda$ quickly as the spin chain length $N$ increases. The transfer fidelity of an excitation at time $t_0$ is independent of $N$ when the system subjects to dissipative environment, while it decreases as $N$ increases when the system subjects to dephasing environment. The average fidelity displays three different patterns corresponding to $N=4r+1$, $N=4r-1$ and $N=2r$. For each pattern, the average fidelity at time $t_0$ is independent of $r$ when the system subjects to dissipative environment, and decreases as $r$ increases when the system subjects to dephasing environment. The maximum concurrence also decreases as $N$ increases, and when $N\rightarrow\infty$, it arrives at an asymptotic value determined by the decoherence rate $\gamma$ and the structure of the spin network.Comment: 12 pages, 6 figure

Non-Markovian entanglement dynamics in coupled superconducting qubit systems

We theoretically analyze the entanglement generation and dynamics by coupled Josephson junction qubits. Considering a current-biased Josephson junction (CBJJ), we generate maximally entangled states. In particular, the entanglement dynamics is considered as a function of the decoherence parameters, such as the temperature, the ratio $r\equiv\omega_c/\omega_0$ between the reservoir cutoff frequency $\omega_c$ and the system oscillator frequency $\omega_0$, % between $\omega_0$ the characteristic frequency of the %quantum system of interest, and $\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels split of the superconducting circuits in the non-Markovian master equation. We analyzed the entanglement sudden death (ESD) and entanglement sudden birth (ESB) by the non-Markovian master equation. Furthermore, we find that the larger the ratio $r$ and the thermal energy $k_BT$, the shorter the decoherence. In this superconducting qubit system we find that the entanglement can be controlled and the ESD time can be prolonged by adjusting the temperature and the superconducting phases $\Phi_k$ which split the energy levels.Comment: 13 pages, 3 figure