Entanglement sudden death in the presence of quantum decoherence in non-inertial frames: beyond the single-mode approximation

The entanglement behavior of Dirac field under quantum decoherence in the non-inertial frames is studied beyond the single-mode approximation. Two kinds of damping processes, amplitude damping channel and dephasing channel, are investigated as the sources of decoherence. The decoherence and Unruh effect will lead to entanglement degradation. This study demonstrates that as two observers experience the decoherence, the entanglement sudden death will occur in amplitude damping channel. Our study shows that the entanglement sudden death will occur in the presence of Unruh effect accompanying the decoherence. In addition, our results show that the amplitude damping channel has more remarkable impacts than the dephasing channel.     

Quantum coherence of fermionic systems in noninertial frames beyond the single-mode approximation

In this paper, we investigate the behavior of the quantum coherence for bipartite fermionic systems in noninertial frames beyond the single-mode approximation. It is shown a redistribution of coherence between particle and antiparticle modes, and the behavior in terms of coherence for fermionic systems is convergent in the infinite acceleration limit. We demonstrate that the physical accessible coherence is not always destroyed with the increase in acceleration, which is different from the features of entanglement in the accelerated frame. Besides, we obtain a quantitative relationship about the redistribution of coherence via the \(l_1\)-norm measure. It is worth mentioning that a rotation operation can change the coherence values, since the amount of coherence is related to the selection of reference basis.     

Quantum coding in non-inertial frames

The quantum and classical correlations are quantified by means of the coherent and mutual information, respectively, where we use the single-mode approximation. It is shown that the users can communicate in an optimal way for small values of accelerations. The capacity of accelerated channel is investigated for different classes of initial states. It is shown that the capacities of the traveling channels depend on the frame in which the accelerated channels are observed in and the initial shared state between the partners. In some frames, the capacities decay as the accelerations of both qubit increase. The decay rate is larger if the partners initially share a maximum entangled state. The possibility of using the accelerated quantum channels to perform quantum coding protocol is discussed. The amount of decoded information is quantified for different cases, where it decays as the partner’s accelerations increase to reach its minimum bound. This minimum bound depends on the initial shared states, and it is large for maximum entangled state.     

Hybrid Fourier–Vlasov simulation in non-inertial reference frames

We present some useful extensions of the spectral Fourier–Vlasov algorithm for simulations of interactions of collisionless plasmas with ion beams. For many practical applications the relative drifts of various particle populations require high resolution of particle distribution functions (PDFs) or the use of large phase space domain, which makes the simulations extremely memory- and time-consuming. We propose using non-inertial reference frames moving in the velocity dimensions for the beam particle distribution functions. As a result, it is possible to simulate plasma–beam interactions at a much lower resolution. This method is particularly suitable for simulations of fast particle beams and plasmas with heavy ion species or cold particle populations. In addition, for simulations of strongly nonlinear instabilities which cause strong plasma heating, the adaptive mesh refinement and phase space reduction are proposed. Contrary to the Vlasov simulation in the real velocity space, plasma heating in the Fourier-inverted space leads to the PDF profile shrinking. Thus, instead of having to extrapolate the PDF into the regions where it was previously undefined, in the Fourier-space, it is sufficient to interpolate the pre-existing solution.     

Decoherence and entanglement degradation of a qubit-qutrit system in non-inertial frames

We study the effect of decoherence on a qubit-qutrit system under the influence of global, local and multilocal decoherence in non-inertial frames. We show that the entanglement sudden death can be avoided in non-inertial frames in the presence of amplitude damping, depolarizing and phase damping channels at lower level of decoherence. However, degradation of entanglement is seen due to Unruh effect. It is seen that for lower values of decoherence, the depolarizing channel heavily degrades the entanglement as compared to the amplitude damping and phase damping channels. Entanglement sudden birth is also seen in case of depolarizing channel. However, for higher values of decoherence parameters, amplitude damping channel dominantly degrades the entanglement of the hybrid system. Entanglement sudden death is not seen for any value of acceleration of the accelerated observer “Rob” in case of phase damping channel. Further more, a symmetrical behaviour of negativity is seen for depolarizing channel.     

Quantum coherence behaviors of fermionic system in non-inertial frame

In this paper, we analyze the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also study the quantum coherence tradeoff between particle and antiparticle sector. It is found that there exists quantum coherence transfer between particle and antiparticle sector, but the coherence lost in particle sector is not entirely compensated by the coherence generation of antiparticle sector. Besides, we emphatically discuss the cohering power and decohering power of Unruh channel with respect to the computational basis. It is shown that cohering power is vanishing and decohering power is dependent of the choice of Unruh mode and acceleration. Finally, we compare the behaviors of quantum coherence with geometric quantum discord and entanglement in relativistic setup. Our results show that this quantifiers in two region converge at infinite acceleration limit, which implies that this measures become independent of Unruh modes beyond the single-mode approximations. It is also demonstrated that the robustness of quantum coherence and geometric quantum discord are better than entanglement under the influence of acceleration, since entanglement undergoes sudden death.     

From Dirac to Diffusion: Decoherence in Quantum Lattice Gases

We describe a model for the interaction of the internal (spin) degree of freedom of a quantum lattice-gas particle with an environmental bath. We impose the constraints that the particle-bath interaction be fixed, while the state of the bath is random, and that the effect of the particle-bath interaction be parity invariant. The condition of parity invariance defines a subgroup of the unitary group of actions on the spin degree of freedom and the bath. We derive a general constraint on the Lie algebra of the unitary group which defines this subgroup, and hence guarantees parity invariance of the particle-bath interaction. We show that generalizing the quantum lattice gas in this way produces a model having both classical and quantum discrete random walks as different limits. We present preliminary simulation results illustrating the intermediate behavior in the presence of weak quantum noise     

Quantum billiards in multidimensional models with fields of forms

A Bianchi type I cosmological model in (n + 1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n ? 1)-dimensional Lobachevsky space ? ^n?1. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quantum billiard for an 11D model with 120 4-forms, whichmimics the SM2-brane sector of D = 11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved.     

Quantum discord protection of a two-qutrit V-type atomic system from decoherence by partially collapsing measurements

In this paper, by exploiting the weak measurement and quantum measurement reversal procedure, we propose a scheme to show how one can protect the geometric quantum discord (GQD) of a two-qutrit V-type atomic system each of which interacts with a dissipative reservoir independently. We examine the scheme for the GQD of the initial two-qutrit Werner and Horodecki states for different classes of weak measurement strengths. It is found out that the presented protocol enables us to suppress decoherence due to the amplitude damping channel and preserve the quantum discord of the two-qutrit system successfully.     

Entanglement dynamics of non-inertial observers in a correlated environment

Effect of decoherence and correlated noise on the entanglement of X-type state of the Dirac fields in the non-inertial frame is investigated. A two qubit X-state is considered to be shared between the partners where Alice is in inertial frame and Rob in an accelerated frame. The concurrence is used to quantify the entanglement of the X-state system influenced by time correlated amplitude damping, depolarizing and bit flip channels. It is seen that amplitude damping and bit flip channels heavily influence the entanglement of the system as compared to the depolarizing channel. It is found possible to avoid entanglement sudden death (ESD) for all the channels under consideration for μ > 0.75 for any type of initial state. No ESD behaviour is seen for depolarizing channel in the presence of correlated noise for entire range of decoherence parameter p and Rob’s acceleration r. It is also seen that the effect of environment is much stronger than that of acceleration of the accelerated partner. Furthermore, it is investigated that correlated noise compensates the loss of entanglement caused by the Unruh effect.     

Dynamic approximation of spatiotemporal receptive fields in nonlinear neural field models

This article presents an approximation method to reduce the spatiotemporal behavior of localized activation peaks (also called "bumps") in non-linear neural field equations to a set of coupled ordinary differential equations (ODEs) for only the amplitudes and tuning widths of these peaks. This enables a simplified analysis of steady-state receptive fields and their stability, as well as spatiotemporal point spread functions and dynamic tuning properties. A lowest-order approximation for peak amplitudes alone shows that much of the well-studied behavior of small neural systems (e.g., the Wilson-Cowan oscillator) should carry over to localized solutions in neural fields. Full spatiotemporal response profiles can further be reconstructed from this low-dimensional approximation. The method is applied to two standard neural field models: a one-layer model with difference-of-gaussians connectivity kernel and a two-layer excitatory-inhibitory network. Similar models have been previously employed in numerical studies addressing orientation tuning of cortical simple cells. Explicit formulas for tuning properties, instabilities, and oscillation frequencies are given, and exemplary spatiotemporal response functions, reconstructed from the low-dimensional approximation, are compared with full network simulations.     

Nonlinearities in the analysis of frames

The material nonlinearity is introduced in the analysis through the representation of the stress-strain variations by continuous functions. The stress function can be adjusted to describe the stress-strain diagrams for various materials such as: steel, aluminum, concrete, etc., by varying the parameters related to the material properties. The continuous variation of the stresses from linear to nonlinear elastic, to plastic states is included in the formulation. For members exhibiting material nonlinearity within some parts of its span, the calculation for the locations of the transition of the stresses from the linear to nonlinear stages is not necessary. The geometrical nonlinearity analysis is also included in the derivations. The analysis can be performed either by an incremental or by an iterative approach, or by using an iterative process within each increment. The third approach is faster and better for structures subjected to high magnitude of nonlinearity. The stability of the structures due to nonlinearities is investigated. A software is modified to include the new formulations. Illustrative examples are provided for the comparisons of the results obtained with those solved previously.     

Studies in a random noise model of decoherence

We study the effects of noise and decoherence for a double-potential well system, suitable for the fabrication of qubits and quantum logic elements. A random noise term is added to the hamiltonian, the resulting wavefunction found numerically and the density matrix obtained by averaging over noise signals. Analytic solutions using the two-state model are obtained and found to be generally in agreement with the numerical calculations. In particular, a simple formula for the decoherence rate in terms of the noise parameters in the two-state model is reviewed and verified for the full simulation with the multi-level system. The formalism is extended to describe multiple sources of noise or different “dephasing” axes at the same time. Furthermore, the old formula for the “Turing-Watched Pot” effect is generalized to the case where the environmental interactions do not conserve the “quality” in question. Various forms for the noise signal are investigated. An interesting result is the importance of the noise power at low frequency. If it vanishes there is, in leading order, no decoherence. This is verified in a numerical simulation where two apparently similar noise signals, but differing in the power at zero frequency, give strikingly different decoherence effects. A short discussion of situations dominated by low frequency noise is given.     

Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, an electromagnetic composite brane ansatz is adopted, and certain restrictions on the branes are imposed, the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases.     

Optimal conditions for Bell-inequality violation in the presence of decoherence and errors

We obtain the set of all detector configurations providing the maximal violation of the Bell inequality in the Clauser–Horne–Shimony–Holt form for a general (pure or mixed) state of two qubits. Next, we analyze optimal conditions for the Bell-inequality violations in the presence of local decoherence, which includes energy relaxation at the zero temperature and arbitrary pure dephasing. We reveal that in most cases the Bell inequality violation is maximal for the “even” two-qubit state. Combined effects of measurement errors and decoherence on the Bell inequality violation are also discussed.     

Comparison of several approaches to the linear approximation of the yield condition and application to the robust design of plane frames for the case of uncertainty

Since the yield condition for frame structures is non-linear, piecewise linear approximations are needed in order to apply linear optimization methods. Four approaches are presented and compared. After the theoretical consideration and comparison of the different approximation methods, they are applied to the robust design of an 18-bar frame in case of uncertainty. Here, the less restrictive methods yield the cheapest design, as expected. It will be shown, that the approximation from inside of first level does not cause much higher costs than the other methods. But since its constraints are sufficient in contrast to other approximations, it is recommended.     

Partial decoherence of histories and the Diósi test

In the decoherent histories approach to quantum theory, attention focuses on the conditions under which probabilities may be assigned to sets of quantum histories. A variety of conditions have been proposed, but the most important one is decoherence, which means that the interference between every pair of histories in the set is zero. Weaker conditions have been considered, such as consistency, or linear positivity, but these are ruled out by the requirement of consistent composition of subsystems, proposed by Diósi. Here we propose a new condition which we call partial decoherence, and is the requirement that every history has zero interference with its negation. This is weaker than decoherence and stronger than linear positivity (but its relation to consistency is less simply defined—it is neither stronger nor weaker). Most importantly, it satisfies the Diósi condition. A strengthened Diósi condition is proposed, which partial decoherence narrowly fails, due to an unusual property of inhomogeneous histories. In an appendix an example is given of a set of histories which are consistent but not decoherent.     

The Dirac Equation in the Kerr-de Sitter Metric

We consider a Fermion in the presence of a rotating BH immersed in a universe with a positive cosmological constant. After presenting a rigorous classification of the number and type of the horizons, we adopt the Carter tetrad to separate the aforementioned equation into radial and angular equations. We show how the Chandrasekhar ansatz leads to the construction of a symmetry operator that in the limit of a vanishing cosmological constant reproduces the square root of the squared total angular momentum operator for a Dirac particle in the Kerr metric. Furthermore, we prove that the the spectrum of the angular operator is discrete and consists of simple eigenvalues, and by means of the functional Bethe ansatz method we also derive a set of necessary and sufficient conditions for the angular operator to have polynomial solutions. Finally, we show that there exist no bound states for the Dirac equation in the non-extreme case.     

On the number of frames in binary words

A frame is a square uu, where u is an unbordered word. Let F(n) denote the maximum number of distinct frames in a binary word of length n. We count this number for small values of n and show that F(n) is at most ⌊n/2⌋+8 for all n and greater than 7n/30−? for any positive ? and infinitely many n. We also show that Fibonacci words, which are known to contain plenty of distinct squares, have only a few frames. Moreover, by modifying the Thue-Morse word, we prove that the minimum number of occurrences of frames in a word of length n is ⌈n/2⌉−2.