Tighter entanglement monogamy relations of qubit systems

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C and the entanglement of formation E. We present new entanglement monogamy relations satisfied by the \(\alpha \)-th power of concurrence for all \(\alpha \ge 2\), and the \(\alpha \)-th power of the entanglement of formation for all \(\alpha \ge \sqrt{2}\). These monogamy relations are shown to be tighter than the existing ones.     

Quantum teleportation between a single-rail single-photon qubit and a coherent-state qubit using hybrid entanglement under decoherence effects

We study quantum teleportation between two different types of optical qubits using hybrid entanglement as a quantum channel under decoherence effects. One type of qubit employs the vacuum and single-photon states for the basis, called a single-rail single-photon qubit, and the other utilizes coherent states of opposite phases. We find that teleportation from a single-rail single-photon qubit to a coherent-state qubit is better than the opposite direction in terms of fidelity and success probability. We compare our results with those using a different type of hybrid entanglement between a polarized single-photon qubit and a coherent state.     

Quantum state control, entanglement, and readout of the Josephson persistent-current qubit

Quantum state control including entanglement, and readout of the Josephson persistent-current qubit, flux qubit, are reviewed. First, we mention our single-shot readout of quantum superposition state of a flux qubit by a current biased dc-SQUID. Second, we mention entangled state and vacuum Rabi oscillations of a flux-qubit LC-resonator system where qubit-resonator coupled state are controlled by a combination of microwave and DC-shift pulses, resulting in a controlling and measuring sequence analogous to atomic cavity QED. Third, we report our recent progress in high fidelity readout of a flux qubit state via Josephson bifurcation amplifier (JBA).     

Geometric phase and entanglement for a single qubit interacting with deformed-states superposition

The geometric phase and quantum entanglement for a nonlinear field-atom system are described quantitatively in terms of different parameters. Specifically, considering a deformed Schrödinger cat interacting with a qubit and taking into account the time dependent of the system coupling. The results show that the initial state setting, atomic motion, photon number and deformation play important roles in the evolution of the system dynamics, nonlocal correlation and geometric phase. An interesting correlation between the entanglement and geometric phase is observed during the time evolution. The presented system is very useful to generate and maintain high amount of entanglement through controlling the phase variation of the system under consideration. We test this observation with experimentally accessible parameters and some new aspects are obtained.     

Quantum dynamics of superconducting nano-circuits: phase qubit, charge qubit and rhombi chains

We have studied different quantum dynamics of superconducting nano-circuits with Josephson junctions. A dc SQUID, when it is strongly decoupled from the environment, demonstrates two-level and multilevel dynamics. We have realized a two qubits coupled circuit based on a dc SQUID in parallel with an asymmetric Cooper pair transistor (ACPT). The ACPT behaves as a charge qubit. Its asymmetry produces a strong tunable coupling with the dc SQUID which is used to realize entangled states between the two qubits and new read-out of the charge qubit based on adiabatic quantum transfer. We have measured the current–phase relations of different rhombi chains in the presence or absence of quantum fluctuations which confirm theoretical predictions.     

Qubit–qubit entanglement dynamics control via external classical pumping and Kerr nonlinearity mediated by a single detuned cavity field powered by two-photon processes

The nonlinear time-dependent two-photon Hamiltonian of a couple of classically pumped independent qubits is analytically solved, and the corresponding time evolution unitary operator, in an exact form, is derived. Using the concurrence, entanglement dynamics between the qubits under the influence of a wide range of effective parameters are examined and, in detail, analyzed. Observations analysis is documented with aid of the field phase-space distribution Wigner function. A couple of initial qubit states is considered, namely similar excited states and a Bell-like pure state. It is demonstrated that an initial Bell-like pure state is as well typical initial qubits setting for robust, regular and a high degree of entanglement. Moreover, it is established that high-constant Kerr media represent an effective tool for generating periodical entanglement at fixed time cycles of maxima reach unity forever when qubits are initially in a Bell-like pure state. Further, it is showed that the medium strength of the classical pumping stimulates efficiently qubits entanglement, specially, when the interaction occurs off resonantly. However, the high-intensity pumping thermalizes the coherent distribution of photons, thus, the least photons number is used and, hence, the least minimum degree of qubits entanglement could be created. Furthermore, when the cavity field and external pumping are detuned, the external pumping acts like an auxiliary effective frequency for the cavity, as a result, the field Gaussian distribution acquires linear chirps, and consequently, more entanglement revivals appear in the same cycle during timescale.     

Effects of cross-Kerr coupling and parametric nonlinearity on normal mode splitting,cooling, and entanglement in optomechanical systems

We study the influence of cross-Kerr (CK) coupling and optical parametric amplifier (OPA) on the effective frequency, damping, normal mode splitting, ground state cooling, and steady state entanglement of an optomechanical system formed by one fixed mirror and one movable mirror. The CK coupling could increase the damping of the movable mirror. The normal mode splitting of the output field is observed due to the CK coupling. The combination of the CK coupling and OPA decreases the minimum attainable phonon number and the effective temperature of the movable mirror. The amount of stationary entanglement between the mechanical and cavity modes can be enhanced by the weak CK coupling. In particular, we find the stationary entanglement becomes more robust against thermal fluctuations of the movable mirror in the presence of the weak CK coupling.     

Parallelism and concurrency of graph manipulations

Graph manipulations are formalized as graph derivations within the framework of graph grammar theory. In this paper we generalize recently published ‘Church–Rosser’ and ‘Parallelism’ Theorems for graph derivations. Given a ‘sequential independent’ sequence of graph derivations G?H ?X the Parallelism Theorem states that there is also a sequential independent sequence via the same productions applied in reverse order, and a direct derivation G ? X via the corresponding parallel production.In our ‘Concurrency Theorem’, the main result of this paper, the assumption of sequential independence is dropped. For each sequence of productions together with dependence relations (allowing later rules to depend on the effects of earlier productions), we construct a single ‘concurrent production’. The Concurrency Theorem states that each graph derivation sequence via the given sequence of productions, which respects all the dependence relations, can be performed in a single direct derivation via the ‘concurrent production’. Moreover this assignment becomes a bijective correspondence.This Concurrency Theorem is formulated and proved in the framework of the algebraic theory of graph grammars using new pushout and pullback lemmas for the 3- and 4- dimensional cubes. As corollaries we obtain the Parallelism Theorem and a theorem reducing the strong to the weak Church–Rosser-property of graph derivations. Applications of these results to various fields in computer science especially to data base systems, are sketched in the introduction.     

Unitary associations method: use of graph theory and computer algorithm

Two species are defined as compatible if their chronologic cooccurrence has been observed (= real association) or can be deduced from biostratigraphic data (= virtual association). An unitary association (U.A.) is a maximal set of compatible species. Each U.A. is characterized by a set of species and/or by a set of species pairs: these characteristic elements are used to identify the U.A. in fossiliferous beds. The U.A.'s which can be identified in a large geographical area are said to be reproducible. A biochronological scale is an ordered sequence of reproducible U.A.'s. The problem of constructing such a discrete “time” scale is approached from a graph-theoretic point of view.     

Direct manipulations of B-spline and NURBS curves

This paper presents a method for the direct manipulations of B-spline and non-uniform rational B-splines (NURBS) curves using geometric constraints. A deformable model is developed to define the deformation energy functional of B-spline and NURBS curves. The finite element method is used to minimize the deformation energy functional and solve for the deformed shape of curves subjected to constraints. This approach results in a set of linear equations for a B-spline curve and a set of non-linear equations for a NURBS curve. A perspective mapping is used to linearize the NURBS formulations. NURBS curves are first mapped from the 3D Cartesian coordinate space to the 4D homogeneous coordinate space, and transformed to 4D B-spline curves. After the manipulation in the 4D homogeneous coordinate space, the modified NURBS curves are then mapped back to the 3D Cartesian coordinate space. The approach is implemented by a prototype program, which is written in C, and runs under WINDOWS. Several examples are presented to demonstrate the capabilities of this approach.     

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.     

Comparing two types of engineering visualizations: task-related manipulations matter

This study focuses on the comparison of traditional engineering drawings with a CAD (computer aided design) visualization in terms of user performance and eye movements in an applied context. Twenty-five students of mechanical engineering completed search tasks for measures in two distinct depictions of a car engine component (engineering drawing vs. CAD model). Besides spatial dimensionality, the display types most notably differed in terms of information layout, access and interaction options. The CAD visualization yielded better performance, if users directly manipulated the object, but was inferior, if employed in a conventional static manner, i.e. inspecting only predefined views. An additional eye movement analysis revealed longer fixation durations and a stronger increase of task-relevant fixations over time when interacting with the CAD visualization. This suggests a more focused extraction and filtering of information. We conclude that the three-dimensional CAD visualization can be advantageous if its ability to manipulate is used.     

Disappearance of entanglement: a topological point of view

We give a topological classification of the evolution of entanglement, particularly the different ways the entanglement can disappear as a function of time. Four categories exhaust all possibilities given the initial quantum state is entangled and the final one is not. Exponential decay of entanglement, entanglement sudden death and sudden birth can all be understood and visualized in the associated geometrical picture - the polarization vector representation. The entanglement evolution categories of any model are determined by the topology of the state space and the dynamical subspace, the limiting state and the memory effect of the environment. Transitions between these types of behaviors as a function of physical parameters are also possible. These transitions are thus of topological nature. The symmetry of the system is also important, since it determines the dimension of the dynamical subspace. We illustrate the general concepts with a visualizable model for two qubits, and give results for extensions to N-qubit GHZ states and W states.     

Teleportation of a qubit using entangled non-orthogonal states: a comparative study

The effect of non-orthogonality of an entangled non-orthogonal state-based quantum channel is investigated in detail in the context of the teleportation of a qubit. Specifically, average fidelity, minimum fidelity and minimum assured fidelity (MASFI) are obtained for teleportation of a single-qubit state using all the Bell-type entangled non-orthogonal states known as quasi-Bell states. Using Horodecki criterion, it is shown that the teleportation scheme obtained by replacing the quantum channel (Bell state) of the usual teleportation scheme by a quasi-Bell state is optimal. Further, the performance of various quasi-Bell states as teleportation channel is compared in an ideal situation (i.e., in the absence of noise) and under different noise models (e.g., amplitude and phase damping channels). It is observed that the best choice of the quasi-Bell state depends on the amount non-orthogonality, both in noisy and noiseless case. A specific quasi-Bell state, which was found to be maximally entangled in the ideal conditions, is shown to be less efficient as a teleportation channel compared to other quasi-Bell states in particular cases when subjected to noisy channels. It has also been observed that usually the value of average fidelity falls with an increase in the number of qubits exposed to noisy channels (viz., Alice’s, Bob’s and to be teleported qubits), but the converse may be observed in some particular cases.     

Robust incoherent control of qubit systems via switching and optimisation

A robust incoherent quantum control scheme via projective measurements plus unitary transformations is proposed for driving a qubit system from an unknown initial mixed state to an arbitrary target pure state. This scheme consists of two main steps: projective measurement on the initial mixed state and optimal control between two pure states. The first step projects the initial state into an eigenstate of the qubit system by projective measurement and guarantees that the proposed scheme is robust to different initial mixed states. The second step finds a set of suitable optimal controls to drive the qubit system from the conditional eigenstate to the target pure state. The connection between the two steps is accomplished by a switching strategy. To accomplish the second step, two approaches are presented in detail. These approaches are time-optimal transition with unbounded control and bang-bang control with minimal switches. The minimal time and minimal number of switches in these approaches can be calculated by simple analytical expressions. The proposed approaches provide two relatively straightforward optimal design methods.     

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.     

Post-Markovian dynamics of quantum correlations: entanglement versus discord

Dynamics of an open two-qubit system is investigated in the post-Markovian regime, where the environments have a short-term memory. Each qubit is coupled to separate environment which is held in its own temperature. The inter-qubit interaction is modeled by XY–Heisenberg model in the presence of spin–orbit interaction and inhomogeneous magnetic field. The dynamical behavior of entanglement and discord has been considered. The results show that quantum discord is more robust than quantum entanglement, during the evolution. Also the asymmetric feature of quantum discord can be monitored by introducing the asymmetries due to inhomogeneity of magnetic field and temperature difference between the reservoirs. By employing proper parameters of the model, it is possible to maintain nonvanishing quantum correlation at high degree of temperature. The results can provide a useful recipe for studying dynamical behavior of two-qubit systems such as trapped spin electrons in coupled quantum dots.     

Security of BB84 with weak randomness and imperfect qubit encoding

The main threats for the well-known Bennett–Brassard 1984 (BB84) practical quantum key distribution (QKD) systems are that its encoding is inaccurate and measurement device may be vulnerable to particular attacks. Thus, a general physical model or security proof to tackle these loopholes simultaneously and quantitatively is highly desired. Here we give a framework on the security of BB84 when imperfect qubit encoding and vulnerability of measurement device are both considered. In our analysis, the potential attacks to measurement device are generalized by the recently proposed weak randomness model which assumes the input random numbers are partially biased depending on a hidden variable planted by an eavesdropper. And the inevitable encoding inaccuracy is also introduced here. From a fundamental view, our work reveals the potential information leakage due to encoding inaccuracy and weak randomness input. For applications, our result can be viewed as a useful tool to quantitatively evaluate the security of a practical QKD system.     

Experimental system design for the integration of trapped-ion and superconducting qubit systems

Quantum Information Processing - We present a design for the experimental integration of ion trapping and superconducting qubit systems as a step towards the realization of a quantum hybrid system....