Non-Markovian entanglement dynamics of two qubits interacting with a common electromagnetic field

We study the non-equilibrium dynamics of a pair of qubits made of two-level atoms separated in space with distance r and interacting with one common electromagnetic field but not directly with each other. Our calculation makes a weak coupling assumption but no Born or Markov approximation. We write the evolution equations of the reduced density matrix of the two-qubit system after integrating out the electromagnetic field modes. We study two classes of states in detail: Class A is a one parameter family of states which are the superposition of the highest energy and lowest energy states, and Class B states which are the linear combinations of the symmetric and the antisymmetric Bell states. Our results for an initial Bell state are similar to those obtained before for the same model derived under the Born–Markov approximation. However, in the Class A states the behavior is qualitatively different: under the non-Markovian evolution we do not see sudden death of quantum entanglement and subsequent revivals, except when the qubits are sufficiently far apart. We provide explanations for such differences of behavior both between these two classes of states and between the predictions from the Markov and non-Markovian dynamics. We also study the decoherence of this two-qubit system.     

Quantum teleportation and dense coding via topological basis

By means of Temperley–Lieb Algebra and topological basis, we make a new realization of topological basis, and get sixteen complete orthonormal topological basis states which are all maximally entangled for four quasi-particles. Then we present an explicit protocol for teleporting an arbitrary two-qubit state via a topological basis entanglement channel. We also show that four bits of classical information can be encoded into a topological basis state by two-particle unitary operations.     

A quantum color image encryption scheme based on coupled hyper-chaotic Lorenz system with three impulse injections

We investigate in detail the dynamics of decoherence, free and bound entanglements, and the conversion from one to another (quantum state transitions), in a two non-interacting qutrits system initially entangled and subject to independents or a common classical noise. Both Markovian and non-Markovian environments are considered. Furthermore, isotropic and bound entangled states for qutrits systems are considered as initial states. We show the efficiency of the formers over the latters against decoherence, and in preserving quantum entanglement. The loss of coherence increases monotonically with time up to a saturation value depending upon the initial state parameter and is stronger in a collective Markov environment. For the non-Markov regime the presence or absence of entanglement revival and entanglement sudden death phenomena is deduced depending on both the peculiar characteristics of the noise, the physical setup and the initial state of the system. We demonstrate distillability sudden death for conveniently selected parameters in bound entangled states; meanwhile, it is completely absent for isotropic states, where entanglement sudden death is avoided for dynamic noise independently of the noise regime and the physical setup. Our results indicate that distillability sudden death under the Markov/non-Markov noise considered can be avoided depending upon the physical setup.

     

A Characterization of Global Entanglement

We define a set of 2 ⁿ⁻¹−1 entanglement monotones for n qubits and give a single measure of entanglement in terms of these. This measure is zero except on globally entangled (fully inseparable) states. This measure is compared to the Meyer–Wallach measure for two, three, and four qubits. We determine the four-qubit state, symmetric under exchange of qubit labels, which maximizes this measure. It is also shown how the elementary monotones may be computed as a function of observable quantities. We compute the magnitude of our measure for the ground state of the four-qubit superconducting experimental system investigated in [M. Grajcar et al., Phys. Rev. Lett. 96, 047006 (2006)], and thus confirm the presence of global entanglement in the ground state.      

Tripartite entanglement sudden death in Yang-Baxter systems

In this paper, we derive unitary Yang-Baxter \breveR(q, j){\breve{R}(\theta, \varphi)} matrices from the 8×8 \mathbbM{8\times8\,\mathbb{M}} matrix and the 4 × 4 M matrix by Yang-Baxteration approach, where \mathbbM/M{\mathbb{M}/M} is the image of the braid group representation. In Yang-Baxter systems, we explore the evolution of tripartite negativity for three qubits Greenberger-Horne-Zeilinger (GHZ)-type states and W-type states and investigate the evolution of the bipartite concurrence for 2 qubits Bell-type states. We show that tripartite entanglement sudden death (ESD) and bipartite ESD all can happen in Yang-Baxter systems and find that ESD all are sensitive to the initial condition. Interestingly, we find that in the Yang-Baxter system, GHZ-type states can have bipartite entanglement and bipartite ESD, and find that in some initial conditions, W-type states have tripartite ESD while they have no bipartite Entanglement. It is worth noting that the meaningful parameter j{\varphi} has great influence on bipartite ESD for two qubits Bell-type states in the Yang-Baxter system.     

Dynamical behavior of quantum correlations between two qubits coupled to an external environment

We investigate the dynamics of quantum correlations of a two-qubit system coupled to an external environment. We have considered both cases: a spin environment and a bosonic environment. In all cases, we have chosen the Bell-diagonal state as the initial state and computed the evolution of quantum correlations in terms of entanglement, quantum discord and trace distance geometric quantum discord. Special attention is paid to the singular quantum phenomena, such as entanglement sudden death, sudden transition and double sudden transitions from classical to quantum decoherence, which all depend on the initial state and the parameters related to the system and the environment. We find the trace distance geometric quantum discord has a good robustness in resisting the spin and bosonic environmental noise.     

Exploring degrees of entanglement

In spite of a long history, the quantification of entanglement still calls for exploration. What matters about entanglement depends on the situation, and so presumably do the numbers suitable for its quantification. Regardless of situational complications, a necessary first step is to make available for calculation some quantitative measure of entanglement. Here we define a geometric degree of entanglement, distinct from earlier definitions, but in the case of bipartite pure states related to that proposed by Shimony (Ann N Y Acad Sci 755:675–679, 1995). The definition offered here applies also to multipartite mixed states, and a variational method simplifies the calculation. We analyze especially states that are invariant under permutation of particles, states that we call bosonic. Of interest to quantum sensing, for bosonic states, we show that no partial trace can increase a degree of entanglement. For some sample cases we quantify the degree of entanglement surviving a partial trace. As a function of the degree of entanglement of a bosonic 3-qubit pure state, we show the range of degree of entanglement for the 2-qubit reduced density matrix obtained from it by a partial trace. Then we calculate an upper bound on the degree of entanglement of the mixed state obtained as a partial trace over one qubit of a 4-qubit bosonic state. As a reminder of the situational dependence of the advantage of entanglement, we review the way in which entanglement combines with scattering theory in the example of light-based radar.     

Asymptotic entanglement in quantum walks from delocalized initial states

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.     

Quantum correlations in Gaussian states via Gaussian channels: steering,entanglement, and discord

Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein–Podolsky–Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.     

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.     

Entanglement observation among single mode bosonic field and an atom

We discuss the atom-field entanglement by proposing a scheme for nonlocality of the atom-field system via nonlocaling the ladder atomic and field operators by a nonlocal unitary operator. It is shown that the standard coherent states of the constructed nonlocal atom-field quantum system are, as an issue of nonlocality, entangled. On the other hand, by proposing a model Hamiltonian for the interacting atom-field system, the standard entangled coherent states can be generated by the dynamical time evolution of the atom-field system.     

Entanglement dynamics during decoherence

The evolution of the entanglement between oscillators that interact with the same environment displays highly non-trivial behavior in the long time regime. When the oscillators only interact through the environment, three dynamical phases were identified (Paz and Roncaglia in Phys Rev Lett 100:220401, 2008) and a simple phase diagram characterizing them was presented. Here we generalize those results to the cases where the oscillators are directly coupled and we show how a degree of mixidness can affect the final entanglement. In both cases, entanglement dynamics is fully characterized by three phases (SD: sudden death, NSD: no-sudden death and SDR: sudden death and revivals) which cover a phase diagram that is a simple variant of the previously introduced one. We present results when the oscillators are coupled to the environment through their position and also for the case where the coupling is symmetric in position and momentum (as obtained in the RWA). As a bonus, in the last case we present a very simple derivation of an exact master equation valid for arbitrary temperatures of the environment.     

Concurrence of three Jaynes–Cummings systems

We apply genuine multipartite concurrence to investigate entanglement properties of three Jaynes–Cummings systems. Three atoms are initially put in GHZ-like state and locally interact with three independent cavities, respectively. We present analytical concurrence expressions for various subsystems including three-atom, three-cavity and some atom-cavity mixed systems. We also examine the global system and illustrate the evolution of its concurrence. Except for the sudden death of entanglement, we find for some initial entanglement parameter \(\theta \), the concurrence of the global system may maintain unchanged in some time intervals.     

Bipartite entanglement of nonlinear quantum systems in the context of the q-Heisenberg Weyl algebra

In this paper, we study in detail the degree of entanglement of bipartite system states in the context of q-Heisenberg-Wely algebra. We examine the entanglement properties for two systems of arbitrary deformation parameters q ₁ and q ₂, defined in entanglement of entangled deformed bosonic coherent states of each of the deformation parameters. For a particular choice of the parameters that specify the coherent states, we give conditions under which bipartite entangled coherent states become maximally entangled. We generalize this formalism to the case of bipartite mixed states using a simplified expression of concurrence in Wootters’ measure of the bipartite entanglement.     

Evolution of quantum correlations in the open quantum systems consisting of two coupled oscillators

The open quantum systems consisting of coupled and uncoupled asymmetric oscillators are considered with an initial quantum-dot trapped-ion coherent state. The quantum correlations between spatial modes of this trapped ion are examined to find their dependence on the temperature, asymmetric parameter, dissipation coefficient and the magnetic field. It is observed that the discord of the initial state is an increasing function of the asymmetric parameter and the magnetic field. Moreover, in the case of two uncoupled modes, entanglement and discord are decreasing functions of temperature and the dissipation coefficient. However, as the temperature and dissipation coefficient increase, the discord fades out faster. In the case of two coupled modes, as the temperature and dissipation coefficient increase, the sudden death of the entanglement and fade out of the discord happen sooner; moreover, as the magnetic field increases, the entanglement sudden death and the discord fade out time occur sooner. Also, with the increase in the asymmetric parameter, the entanglement sudden death is postponed. In addition, in the asymmetric system, appreciable discord can be created in the temperature range 0–10 K, while appreciable entanglement can be created in the temperature range 0–5 mK. Finally, it is observed that non-monotonic evolution of quantum correlations is due to coupling of modes.     

Tripartite entanglement dynamics in the presence of Markovian or non-Markovian environment

We study on the tripartite entanglement dynamics when each party is initially entangled with other parties, but they locally interact with their own Markovian or non-Markovian environment. First we consider three GHZ-type initial states, all of which have GHZ-symmetry provided that the parameters are chosen appropriately. However, this symmetry is broken due to the effect of environment. The corresponding \(\pi \)-tangles, one of the tripartite entanglement measures, are analytically computed at arbitrary time. For Markovian case while the tripartite entanglement for type I exhibits an entanglement sudden death, the dynamics for the remaining cases decays normally in time with the half-life rule. For non-Markovian case the revival phenomenon of entanglement occurs after complete disappearance of entanglement. We also consider two W-type initial states. For both cases the \(\pi \)-tangles are analytically derived. The revival phenomenon also occurs in this case. On the analytical ground the robustness or fragility issue against the effect of environment is examined for both GHZ-type and W-type initial states.     

Quantifying entanglement of two relativistic particles using optimal entanglement witness

In a recent paper, it was shown that the projections of a relativistic spin operator (RSO) massive spin- \frac12{\frac{1}{2}} particle on a world-vector which can be in timelike or null tetrad direction are proportional to the helicity or Bargman-Wigner (BW) qubit, respectively. Here we consider Lorentz transformations of two-particle states, which have been constructed both in helicity basis. For convenience, instead of using the superposition of momenta we use only two momentum eigenstates (p ₁ and p ₂) for each particle. Consequently, in 2D momentum subspace we describe the structure of one particle in terms of the four-qubit system. We present a new approach to quantification of relativistic entanglement based on entanglement witness (EW), which is obtained by a new method of convex optimization. In addition, Lorentz invariance of entanglement using BW qubit is also studied.     

Beam splitting and entanglement generation: excited coherent states

We study the mathematical properties of the excited coherent states, which are obtained through actions of a photon creation operator of the mode optical field on its corresponding coherent state, by analyzing the minimal set of Klauder’s coherent states. Using linear entropy as a measure of entanglement, we investigate in detail the entanglement generated via a beam splitter when an excited coherent state is injected on one input mode and vacuum state is injected on the other one. Finally, we examine the physical properties of the excited coherent states through the Mandel’s parameter and the Wehrl entropy and we give the correlation between these parameters and the entanglement of the output state.     

Positiveness of dynamic systems with nonpositive coefficientmatrices

This note gives a dynamical solution for linear dynamical feasibility problems, and applies this result to a generalization of the concept of positive systems. More specifically, we require the existence of a positive state and/or output evolution for any initial state in a given set. We give conditions for various sets of initial states. Finally, by means of an example, we illustrate our results     

Reversibility of Local Transformations of Multiparticle Entanglement

We consider the transformation of multisystem entangled states by local quantum operations and classical communication. We show that, for any reversible transformation, the relative entropy of entanglement for any two parties must remain constant. This shows, for example, that it is not possible to convert 2N three-party GHZ states into 3N singlets, even in an asymptotic sense. Thus there is true three-party non-locality (i.e. not all three party entanglement is equivalent to two-party entanglement). Our results also allow us to make quantitative. statements about concentrating multi-particle entanglement. Finally, we show that there is true n-party entanglement for any n.