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Entanglement exhibits a unique property of quantum theory that is unseen in classical counterparts. The experimental confirmation of Bell’s inequalities has surprised many people and revived interest and debate regarding the exact nature of quantum theory, including the wave-particle duality. On the other hand, rapid advancements in computing technology in recent years have provided a new tool for investigating the nature of quantum theory. In this paper, numerical simulation is used to visualize the nonlocality implied in quantum entanglement. In particular, a Gedanken experiment of a discrete approximation of a continuous quantum space is provided, similar to the case of the dual nature of particle/wave in the double-slit experiment. The results are expected to provide a different angle for a deeper understanding of the mysterious nature of quantum correlations.

Multi-hop teleportation is a quantum teleportation scheme for transferring quantum states on a large scale. In this paper, a new multi-hop teleportation protocol is investigated for transferring arbitrary N-qubit states between M-neighbor nodes. In this scheme, intermediate nodes are connected with each other by symmetric entangled Bell states as quantum channels. First, one-hop teleportation of single-qubit, two-qubit and N-qubit states are introduced, then this method is generalized to two-hop and multi-hop teleportation for N-qubit. Also, we calculate the efficiency of this scheme.

With the development of lab technology, the low-order correlation function can no longer describe the main effect of decoherence in the quantum many-body system, so it is imperative to study the higher-order correlation function of the system. In this paper, the higher-order correlation function is discussed analytically in the 1D transverse Ising model, and it is searched when the third-order or higher correlation functions play a key role in the decoherence effect. Under the cases of strong coupling and long coherence time, it is indicated that the effect of high-order correlation functions cannot be ignored, and the approximation of the classical Markov process is limited. But the low-order correlation function can describe well in the case of weak coupling and short coherence time.

It is well known that the maximal violation of the Bell’s inequality for a two-qubit system is related to the entanglement formation in terms of a concurrence. However, a generalization of this relation to an $n$-qubit state has not been found. In this paper, we demonstrate some extensions of the relation between the upper bound of the Bell’s violation and a generalized concurrence in several $n$-qubit states. In particular, we show the upper bound of the Bell’s violation can be expressed as a function of the generalized concurrence, if a state can be expressed in terms of two variables. We apply the relation to the Wen-Plaquette model and show that the topological entanglement entropy can be extracted from the maximal Bell’s violation.

In this work, a gauge approach to quantum computing is considered. It is assumed that there exists a classical procedure for placing certain classical system in a state described by a holomorphic vector bundle with connection with logarithmic singularities. This bundle and its connection are constructed with the aid of unitary operators realizing the given algorithm using methods of the monodromic Riemann–Hilbert problem. Universality is understood in the sense that for any collection of unitary matrices there exists a connection with logarithmic singularities whose monodromy representation involves these matrices.

We present an approach that allows quantifying decoherence processes in an open quantum system subject to external time-dependent control. Interactions with the environment are modeled by a standard bosonic heat bath. We develop two unitarity-preserving approximation schemes to calculate the reduced density matrix. One of the approximations relies on a short-time factorization of the evolution operator, while the other utilizes expansion in terms of the system-bath coupling strength. Applications are reported for two illustrative systems: an exactly solvable adiabatic model, and a model of a rotating-wave quantum-computing gate function. The approximations are found to produce consistent results at short and intermediate times.

The speed of quantum computation is investigated through the time evolution of the speed of the orthogonality. The external field components for classical treatment besides the detuning and the coupling parameters for quantum treatment play important roles on the computational speed. It has been shown that the number of photons has no significant effect on the speed of computation. However, it is very sensitive to the variation in both detuning and the interaction coupling parameters.

Breather is an elementary excitation regarded as a bound state of a fluxon and an antifluxon in a long Josephson junction. In quantum-mechanical regime, the breather energy is quantized so that the breather can be considered as an artificial moving atom. We propose a new type of fluxon qubit that is constructed by quantum-mechanical superposition of the breather's states. We describe quantum logic gates of breather qubit required for constructing quantum computer. In addition, our qubit can move in the system so that transfer of quntum information is possible between mobile qubits as well as stationary qubits. Our talking qubits support the global information sharing in quantum information networks.

In the present paper, an influence of the anisotropic antisymmetric exchange interaction, the Dzialoshinskii–Moriya (DM) interaction, on entanglement of two qubits in various magnetic spin models, including the pure DM model and the most general XYZ model, are studied. We find that the time evolution generated by DM interaction can implement the SWAP gate and discuss realistic quasi-one-dimensional magnets where it can be realized. It is shown that inclusion of the DM interaction to any Heisenberg model creates, when it does not exist, or strengthens, when it exists, the entanglement. We give physical explanation of these results by studying the ground state of the systems at T = 0. Nonanalytic dependence of the concurrence on the DM interaction and its relation with quantum phase transition is indicated. Our results show that spin models with the DM coupling have some potential applications in quantum computations and the DM interaction could be an efficient control parameter of entanglement.

The four-level entangled quantum refrigerator (QR) is studied in the XXZ Heisenberg model for the two-qubits. The Hamiltonian of the problem includes the exchange parameters J_x = J_y = J and J_z = αJ along the x-, y- and z-directions, respectively, and constant external magnetic field B in the z-direction. The parameter α is introduced into the model which controls the strength of the exchange parameter J_z in comparison to J_x and J_y, thus, our investigation of QR includes the XX (α = 0.0), XXX (α = 1.0) and XXZ (for other α's) Heisenberg models. The two-qubits are assumed to be in contact with two heat reservoirs at different temperatures. The concurrences for a two-qubit are used as a measure of entanglement and then the expressions for the amount of heat transferred, the work performed and the efficiency are derived. The contour, i.e., the isoline maps, and some two-dimensional plots of the above mentioned thermodynamic quantities are illustrated.

Correlations in open quantum systems exhibit peculiar phenomena under the effect of various sources of noise. Here, we investigate the dynamics of entanglement and quantum discord (QD) for three noninteracting qubits coupled with a classical environmental static noise characterized by an external random field. Two initial entangled states of the system are examined, namely, the GHZ- and $W$-type states. The system-environment interaction is here analyzed in three different configurations, namely, independent, mixed and common environments. We find that the dynamics of quantum correlations are strongly affected by the type of system-environment interaction and the purity of the initial entangled state. Indeed, depending on the type of interaction and the value of the purity of the initial state, peculiar phenomena such as sudden death, revivals and long-time survival of quantum correlations are observed. On the other hand, our results clearly show that quantum correlations initially present in the $W$-type states are less robust than those of the GHZ-type states. Furthermore, we find that the long-time survival of entanglement can be detected by means of the suitable entanglement witnesses.

Low-dimensional complex oxides offer new opportunities for small-scale electronic devices where diverse spin, charge and orbital correlations can be suitably adapted by manipulating many-body interactions, geometries, disorder, fields, strain, etc. Therefore, oxides may be viewed as one of the promising candidates for replacing semiconductors in future devices. Maintaining coherence and control in a qubit is an important necessity for quantum computation. In this review, we discuss an example of oxide devices: decoherence-free oxide-based qubits. We present recent progress in demonstrating that long coherence times can be achieved at easily accessible temperatures in charge qubits of oxide double quantum dots. For treating strong coupling to the environment, we describe a nonperturbative approach that is useful for oxides. We illustrate ways to enhance the coherence times: increasing the electron–phonon coupling, detuning the dots to a fraction of the optical phonon energy, decreasing the temperature or reducing the adiabaticity.

The influences of the dispersion, the impurity and the electron–phonon coupling (EPC) on the properties of the Gaussian confining (GC) potential qubit with magnetic field were studied by Pekar-type variation method. Results show that the decoherence time will increase with increasing the dielectric constant (DC) ratio, the dispersion coefficient and the EPC strength, respectively. The phase rotation quality factor increases with increasing the dielectric constant ratio, the dispersion coefficient and EPC strength, respectively. The magnetic field has a regulatory effect on the decoherence time and the phase rotation quality factor.

The quantization scheme between double enhanced charge phase-slip (ECPS) qubits is given. In this system, there exist quantum entanglement phenomenona. The entanglement characteristic is discussed by employing the concurrence. An interesting conclusion is obtained, i.e., if one desire to change the entanglement between two ECPS qubits, the mutual inductance should be considered first, but it is also a good choice to tune symmetric and asymmetric combination of two gate voltages.

In this paper we calculate the loss of fidelity due to quantum leakage for the Josephson charge qubit (JCQ). In this investigation the characteristic values and characteristic states of the Mathieu equation are used. It is shown that for present typical parameters of JCQ, E_J/E_ch ~ 0.02, the loss of the fidelity per elementary operation is about 10^-4 which satisfies DiVincenzo's low decoherence criterion. By appropriately improving the designs of the Josephson junction, namely, decreasing E_J/E_ch to ~ 0.01, the loss of fidelity per elementary operation can decrease even smaller to 10^-5. The first-order nonadiabatic correction is also obtained by using the approach.

We investigate the mutual information and entanglement of stationary states of two locally driven qubits under the influence of collective dephasing. It is shown that both the mutual information and the entanglement of two qubits in the stationary state exhibit damped oscillation with the scaled action time γT of the local external driving field. It means that we can control both the entanglement and total correlation of the stationary state of two qubits by adjusting the action time of the driving field. We also consider the influence of collective dephasing on the entanglement of two qutrits and obtain the sufficient condition that the stationary state is entangled.

N rotations can be teleported simultaneously onto a group of remote qubits deterministically or probabilistically with the aid of an entangled qudit pair. We present a scheme for such a kind of remote control of quantum gate. We are mainly focused on the remote rotation around a fixed axis. We first present an explicit scheme for deterministically and exactly teleporting the N rotations by using a maximally entangled qudit pair as quantum channel. We also put forward a scheme for probabilistically implementing the N remote rotations with unit fidelity by employing a partially entangled qudit pair as the quantum channel. An analysis of the scheme indicates that use of partially entangled quantum channel for teleporting the N rotations leads to the problem of "the general optimal information extraction".

On the condition of electron–LO-phonon strong coupling in an anisotropic qunntum dot (QD), the eigenenergies of the ground-state and the first excited state, the eigenfunctions of the ground-state and the first excited state are obtained by using a variational method of Pekar type. This system in QD may be employed as a quantum system-qubit. Numerical calculations are performed on the pure dephasing factor. The relations of the pure dephasing factor on the temperature, the Coulomb binding parameter, the electron–LO-phonon coupling strength and the effective confinement length are derived.

We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Our numerical results indicate that the decoherence rate will decrease with increasing the confinement length of the quantum dot (QD) and decrease with increasing electron-LO-phonon coupling constant. The influences of the polar angle on the decoherence rate are dominant when the coupling constant increases, while the effects of the polar angle on that are strong when the confinement length increases. Meanwhile, the decoherence rate varies periodically with respect to the polar angle.

We consider the time evolution of a two level system (a two level atom or a qubit) and show that it is characterized by a local (in time) gauge invariant evolution equation. The covariant derivative operator is constructed and related to the free energy. We show that the gauge invariant characterization of the time evolution of the two level system is analogous to the birefringence phenomenon in optics. The relation with Berry-like and Anandan–Aharonov phase is pointed out. Finally, we discuss entropy, environment effects and the distance in projective Hilbert space between two level states in their evolution.