Directional quantum random walk induced by coherence

Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a non-binomial position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.     

Entanglement swapping between electromagnetic field modes and matter qubits

Scalable quantum networks require the capability to create, store and distribute entanglement among distant nodes (atoms, trapped ions, charge and spin qubits built on quantum dots, etc.) by means of photonic channels. We show how the entanglement between qubits and electromagnetic field modes allows generation of entangled states of remotely located qubits. We present analytical calculations of linear entropy and the density matrix for the entangled qubits for the system described by the Jaynes-Cummings model. We also discuss the influence of decoherence. The presented scheme is able to drive an initially separable state of two qubits into an highly entangled state suitable for quantum information processing.     

One-dimensional quantum walks with a position-dependent coin

We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle, which depends upon the position of a quantum particle, parameterizes the coin operator. For different values of the rotation angle, we observe that such a coin leads to a variety of probability distributions, e.g. localized, periodic, classicallike, semi-classical-like, and quantum-like. Further, we study the Shannon entropy associated with position and the coin space of a quantum particle, and compare them with the case of the position-independent coin. Our results show that the entropy is smaller for most values of the rotation angle as compared to the case of the position-independent coin. We also study the effect of entanglement on the behavior of probability distribution and Shannon entropy by considering a quantum walk with two identical position-dependent entangled coins. We observe that in general, a wave function becomes more localized as compared to the case of the positionindependent coin and hence the corresponding Shannon entropy is lower. Our results show that a position-dependent coin can be used as a controlling tool of quantum walks.     

Entanglement reciprocation between qubits and continuous variables

We investigate how entanglement can be transferred between qubits and continuous-variable (CV) systems. We find that one ebit borne in maximally entangled qubits can be fully transferred to two CV systems which are initially prepared in a pure separable Gaussian field with high excitation. We show that it is possible to retrieve the entanglement back to qubits from the entangled CV systems. The deposition of multiple ebits from qubits to the initially separable CV systems is also pointed out. We show that the entanglement transfer and retrieval are done at a quasisteady state.     

Mutual preservation of entanglement

We study a generalized double Jaynes–Cummings (JC) model where two entangled pairs of two-level atoms interact indirectly. We show that there exist initial states of the qubit system so that two entangled pairs are available at all times. In particular, the minimum entanglement in the pairs as a function of the initial state is studied. Finally, we extend our findings to a model consisting of multi-mode atom–cavity interactions. We use a non-Markovian quantum state diffusion (QSD) equation to obtain the steady-state density matrix for the qubits. We show that the multi-mode model also displays dynamical preservation of entanglement.     

Exact Entanglement Dynamics in Three Interacting Qubits

Motivated by recent experimental studies on coherent dynamics transfer in three interacting atoms or electron spins [Phys. Rev. Lett 114(2015) 113002, Phys. Rev. Lett 120(2018) 243604], here we study entanglement entropy transfer in three interacting qubits. We analytically calculate time evolutions of wave function, density matrix and entanglement of the system. We find that initially entangled two qubits may alternatively transfer their entanglement entropy to other two qubit pairs. Thus dynamical evolution of three interacting qubits may produce a genuine three-partite entangled state through entanglement entropy transfers. In particular, different pairwise interactions of the three qubits endow symmetric and asymmetric evolutions of the entanglement transfer,characterized by the quantum mutual information and concurrence. Finally, we discuss an experimental proposal of three Rydberg atoms for testing the entanglement dynamics transfer of this kind.     

A Macroscopic Device for Quantum Computation

We show how a compound system of two entangled qubits in a non-product state can be described in a complete way by extracting entanglement into an internal constraint between the two qubits. By making use of a sphere model representation for the spin 1/2, we derive a geometric model for entanglement. We illustrate our approach on 2-qubit algorithms proposed by Deutsch, respectively Arvind. One of the advantages of the 2-qubit case is that it allows for a nice geometrical representation of entanglement, which contributes to a more intuitive grasp of what is going on in a 2-qubit quantum computation.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Generation of Entanglement Between Two Noninteracting Qubits via Interaction with Nonclassical Radiation Field

We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes-Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.     

Relativity of quantum states in entanglement swapping

The entanglement swapping protocol is analyzed in a relativistic setting, where shortly after the entanglement swapping is performed, a Bell test is performed. For an observer in the laboratory frame, a Bell violation is observed between the qubits with the swapped entanglement. In a moving frame, the order of the measurements is reversed, and a Bell violation is observed even though the particles are not entangled, directly or indirectly, or at any point in time. Although the measurement results are identical, the wavefunctions for the two frames are starkly different — one is entangled and the other is not. Furthermore, for boosts in a perpendicular direction, in the presence of decoherence, we show that the maximum Bell violation can occur across non-simultaneous points in time. This is a signature of entanglement that is spread across both space and time, showing both non-local and non-simultaneous aspects of entanglement.     

Estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes

The paper investigates the estimation of the disorder degree of the classical static noise using three entangled qubits as quantum probes together with the tools of local quantum estimation theory. Three probing schemes namely common environment (CE), independent environments (IEs) and mixed environments (MEs) are investigated and the optimal initial state preparation of the probes taken as a partially depolarized GHZ state. The results show that: (i) the IEs probing scheme allows one to achieve better estimation precision compared to both MEs and CE schemes respectively; (ii) the higher is the initial amount of entanglement of the probes, the larger is the estimation precision, independently of the scheme considered; (iii) both small and large values of the disorder parameter are uniformly estimable at the optimal interaction time; (iv) entangled qubits probes quickly encode information about the disorder parameter than single-qubit probe; (v) there is an improvement in the estimation of the disorder parameter when entangled probes interacting either in IEs or MEs are used instead of a single probe, demonstrating that a single probe is not sufficient to optimally estimate the disorder parameter of the static noise. On the other hand, we have also investigated the relationship between the residual amount of entanglement present in the probes at the optimal interaction time and the estimation precision of the disorder parameter. We show that the higher the residual amount of entanglement at the optimal interaction time, the smaller the estimation precision.     

Entanglement dynamics of qubits in a common environment

We use the quantum jump approach to study the entanglement dynamics of a quantum register, which is composed of two or three dipole-dipole coupled two-level atoms, interacting with a common environment. Our investigation of entanglement dynamics reflects that the environment has dual actions on the entanglement of the qubits in the model. While the environment destroys the entanglement induced by the coherent dipole-dipole interactions, it can produce stable entanglement between the qubits prepared initially in a separable state. The analysis shows that it is the entangled decoherence-free states contained as components in the initial state that contribute to the stable entanglement. Our study indicates how the environmental noise produces the entanglement and exposes the interplay of environmental noise and coherent interactions of qubits on the entanglement.     

Synthesis of maximally entangled mixed states and disentanglement in coupled Josephson charge qubits

We analyze a controllable generation of maximally entangled mixed states of a circuit containing two-coupled superconducting charge qubits. Each qubit is based on a Cooper pair box connected to a reservoir electrode through a Josephson junction. Illustrative variational calculations were performed to demonstrate the effect on the two-qubits entanglement. At sufficiently deviation between the Josephson energies of the qubits and/or strong coupling regime, maximally entangled mixed states at certain instances of time is synthesized. We show that entanglement has an interesting subsequent time evolution, including the sudden death effect. This enables us to completely characterize the phenomenon of entanglement sharing in the coupling of two superconducting charge qubits, a system of both theoretical and experimental interest.     

Induced entanglement revival and entanglement protection in a two qubit system

A system of two initially entangled qubits interacting with a bosonic environment is considered. The interaction induces a loss of the initial entanglement of the two qubits, and for specific initial states it causes entanglement sudden death. An investigation of the modifications on the entanglement dynamics by a single pulse control field, performed in the two qubit system, shows that the control field can not only protect entangled states against sudden death but also induce a revival of entanglement in the two qubit system.     

Some New Solutions of Jacobi Elliptic Functions to mBBM Equation

The modified mapping method is further improved by the expanded expression of u（ξ） that contains the terms of the first-order derivative of function f（ξ）. Some new exact solutions to the mBBM equation are determined by means of the method. We can obtain many new solutions in terms of the Jacobi elliptic functions of the equation.     

Entanglement reciprocation between two charge qubits and two-cavity field

We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits, we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.     

Entanglement reciprocation between two charge qubits and two-cavity field

We propose a simple scheme to generate two-mode entangled coherent state in two separated cavities and realize the entanglement reciprocation between the superconducting charge qubits and continuous-variable system. By measuring the state of charge qubits, we find that the entanglement of two charge qubits, which are initially prepared in the maximally entangled state, can be transferred to the two-cavity field, and at this time the two-cavity field is in the entangled coherent state. We also find that the entanglement can be retrieved back to the two charge qubits after measuring the state of the two-cavity field.      

Entanglement Transfer via Heisenberg Interaction in a Four-Qubit System

We investigate the entanglement transfer in a four-qubit system and calculate the concurrence between any two qubits in different initial states. We show that both the pure entangled state and mixed entangled state can be transferred. For some special coupling constants and some evolution time, entanglement can be completely transferred from one pair particles to another.     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.     

Entangled quantum heat engines based on two two-spin systems with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

We construct an entangled quantum heat engine (EQHE) based on two two-spin systems with Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction. By applying the explanations of heat transferred and work performed at the quantum level in Kieu’s work [Phys. Rev. Lett. 93, 140403 (2004)], the basic thermodynamic quantities, i.e., heat transferred, net work done in a cycle and efficiency of EQHE are investigated in terms of DM interaction and concurrence. The validity of the second law of thermodynamics is confirmed in the entangled system. It is found that there is a same efficiency for both antiferromagnetic and ferromagnetic cases, and the efficiency can be controlled in two manners: (1) only by spin-spin interaction J and DM interaction D; (2) only by the temperature T and concurrence C. In order to obtain a positive net work, we need not entangle all qubits in two two-spin systems and we only require the entanglement between qubits in a two-spin system not be zero. As the ratio of entanglement between qubits in two two-spin systems increases, the efficiency will approach infinitely the classical Carnot one. An interesting phenomenon is an abrupt transition of the efficiency when the entanglements between qubits in two two-spin systems are equal.