Generic entanglement and standard form for N-mode pure Gaussian states

We investigate the correlation structure of pure N-mode Gaussian resources which can be experimentally generated by means of squeezers and beam splitters, whose entanglement properties are generic. We show that those states are specified (up to local unitaries) by N(N-1)/2 parameters, corresponding to the two-point correlations between any pair of modes. Our construction yields a practical scheme to engineer such generic-entangled N-mode pure Gaussian states by linear optics. We discuss our findings in the framework of Gaussian matrix product states of harmonic lattices, raising connections with entanglement frustration and the entropic area law.     

Estimating entanglement measures in experiments

We present a method to estimate entanglement measures in experiments. We show how a lower bound on a generic entanglement measure can be derived from the measured expectation values of any finite collection of entanglement witnesses. Hence witness measurements are given a quantitative meaning without the need of further experimental data. We apply our results to a recent multiphoton experiment [M. Bourennane, Phys. Rev. Lett. 92, 087902 (2004)], giving bounds on the entanglement of formation and the geometric measure of entanglement in this experiment.     

Entanglement of fermions at quantum criticality

The study of entanglement properties of quantum critical many-particle systems has become a subject of intense interest. While the basic features of entanglement scaling for critical spin-1/2 systems (coupled qubits) are by now fairly well understood, entanglement properties of critical fermions (or bosons) are less well studied. In an effort to contribute to this problem, we have analyzed the single-site entanglement of a generic spin-1/2 lattice fermion system and found that (under certain provisos) this measure can be used as a reliable marker to identify and partly characterize a quantum critical point. We illustrate our findings by exact analytical results for the single-site entanglement at the magnetic and Mott-Hubbard transitions of the 1D Hubbard model and at the Mott-Hubbard transitions of the 1D Hubbard model with long-range hopping. The text was submitted by the authors in English.     

非均匀外磁场下海森堡自旋链的热纠缠

研究了两量子比特海森堡XXX自旋链处于x方向的非均匀磁场时系统的纠缠特性,并用负度N来度量.得到N的解析表达式,并在此基础上进行数值计算.仔细讨论了均匀磁场B、非均匀磁场b、温度T和自旋耦合系数J对纠缠度N的影响.结果表明:N会随着■和T的增大而减小,但会随着J的增大而增大.同时,增大的J和b还会使临界磁场■和临界温度T_th变大,从而使系统中热纠缠存在的磁场范围和温度范围都变大.这一点在较大磁场和较高温度下需要纠缠具有实际意义.由此,我们可以通过调节B、b、T和J来控制热纠缠,这对固态系统中通过构建和选择参数调整系统的纠缠度具有一定的作用和意义.     

Persistent entanglement in arrays of interacting particles

We study the entanglement properties of a class of N-qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They also have a high persistency of entanglement which means that approximately N/2 qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of 相似文献   

自旋为1的海森堡XX链的杂质纠缠

采用Negativity研究了匀强磁场下自旋为1的3-qutrit海森堡XX模型的基态纠缠和热纠缠. 分别探讨了纠缠伴随杂质, 温度、磁场的变化情况. 研究表明磁场的作用主要是降低纠缠, 磁场并不改变临界温度. 杂质的加入有利于增加纠缠, 临界温度的改变来自杂质参数J₁的变化. 可以通过调节温度T, 杂质参数J₁和磁场B来控制纠缠.     

Evolution of entanglement between magnetic moments under interaction with tunneling current

We investigate the evolution of entanglement between two magnetic moments which are initially independent and interact with electron current tunneling through them. The magnetic moments may be nanomagnets, magnetic atoms or atom clusters with spins larger than \frac12\frac{1}{2}. The tunneling of electrons through two moments can be realized by equally coupling two leads (electron reservoirs) to them and applying bias voltage to the leads. In the sequential regime the effect of electron current on the entanglement is calculated fully quantum-mechanically by using extended scattering-matrix theory. It is found that under certain conditions the entanglement can be enhanced from zero to unity by applying the current. We investigate the dependence of the entanglement on the interaction strength and the value of the moments. We discuss the favorite conditions for the realization of entangling gates using such setup.     

Fidelity and entanglement breaking properties of qutrit channels

We investigate fidelity and entanglement breaking properties of quantum qutrit channels. We focus on channel fidelity evaluated for pure initial states and entanglement fidelity for purified mixed states (or pure entangled qutrit states) and use negativity as an entanglement measure for qutrits. We analyze properties of qutrit gates and channels based on affine transformations of qutrit Bloch vectors. We employ channel complete positivity constraints into the discussion of fidelity and entanglement behaviour.     

不同方向外磁场下海森堡自旋链的热纠缠

研究了两量子比特的海森堡XXX自旋链分别处于x方向和y方向均匀外磁场时系统的纠缠特性,并用负度N来度量。得到纠缠度N的解析表达式,并在此基础上进行数值计算。仔细讨论了磁场B、温度T和自旋耦合系数J对纠缠度N的影响。结果表明：纠缠度N会随着磁场|B|和温度T的增大而减小,但会随着自旋耦合系数J的增大而增大。另外,增大的J还会使临界磁场|Bc|和临界温度Tth变大。所以,我们可以通过调节B、T和J来控制热纠缠,这对固态系统中通过构建和选择参数调整系统的纠缠度具有一定的作用和意义。研究还发现,加在x方向均匀外磁场和加在y方向均匀外磁场对两量子比特的海森堡XXX自旋链的作用效果是一样的。     

Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Quantum information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled, but the homonuclear spins often become strongly coupled. In such circumstances, the strongly coupled spins, which yield second order spectra, can no longer be individually treated as qubits. However, it has been demonstrated elsewhere, that the 2(N) energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement, and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.     

Quantum circuits for controlled teleportation of two-particle entanglement via a W state

A protocol for three-party controlled quantum teleportation is discussed. It is shown that an unknown two-particle entanglement can be teleported to any one of two receivers via the only one three-particle W state. We summarize all different unitary transformations performed by the receiver with a concise formula. The quantum circuits for the generalized measurement described by positive operator-valued measure (POVM), which is utilized to probabilistically distinguish the two non-orthogonal states, are explicitly constructed by means of quantum Toffoli gates. The efficient quantum circuits for implementing the teleportation are also provided.     

Efficient entanglement purification in quantum repeaters

We present an efficient entanglement purification protocol(EPP) with controlled-not(CNOT) gates and linear optics.With the CNOT gates,our EPP can reach a higher fidelity than the conventional one.Moreover,it does not require the fidelity of the initial mixed state to satisfy F > 1/2.If the initial state is not entangled,it still can be purified.With the linear optics,this protocol can get pure maximally entangled pairs with some probabilities.Meanwhile,it can be used to purify the entanglement between the atomic ensembles in distant locations.This protocol may be useful in long-distance quantum communication.     

Distributed entanglement generation from asynchronously excited qubits

The generation of GHZ states calls for simultaneous excitation of multiple qubits. The peculiarity of such states is reflected in their nonzero distributed entanglement which is not contained in other entangled states. We study the optimal way to excite three superconducting qubits through a common cavity resonator in a circuit such that the generation of distributed entanglement among them could be obtained at the highest degree in a time-controllable way. A non-negative measure quantifying this entanglement is derived as a time function of the quadripartite system evolution. We find that this measure does not stay static but obtains the same maximum periodically. When the qubit-resonator couplings are allowed to vary, its peak value is enhanced monotonically by increasing the greatest coupling strength to one of the qubits. The period of its peak to peak revival maximizes when the couplings become inhomogeneous, thus qubit excitation becoming asynchronous, at a relative ratio of 0.35. The study demonstrates the role of asynchronous excitations for time-controlling multi-qubit systems, in particular in extending entanglement time.     

Improvement on controlled-controlled-NOT operation-based entanglement purification protocol

We show that controlled-controlled-NOT(CCN)operation-based entanglement purification protocol can be further improved.CCN protocol requires Bell state measurements after performing the CCN operations.In the original CCN protocol,the measured states are assumed to be destroyed.However,if controlled-NOT gates are used to perform such Bell state measurements,in some unsuccessful situations of the CCN protocol,one can further purify the two mixed entangled states which are to be measured.In this way,the total efficiency of the CCN protocol is further increased.     

Efficient entanglement purification in quantum repeaters

We present an efficient entanglement purification protocol (EPP) with controlled-not (CNOT) gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy F>1/2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.     

Bound entanglement and continuous variables

We introduce the definition of generic bound entanglement for the case of continuous variables. We provide some examples of bound entangled states for that case, and discuss their physical sense in the context of quantum optics. We raise the question of whether the entanglement of these states is generic. As a by-product we obtain a new many parameter family of bound entangled states with positive partial transpose. We also point out that the "entanglement witnesses" and positive maps revealing the corresponding bound entanglement can easily be constructed.     

Density of states of quantum spin systems from isotropic entanglement

We propose a method that we call isotropic entanglement (IE), which predicts the eigenvalue distribution of quantum many body (spin) systems with generic interactions. We interpolate between two known approximations by matching fourth moments. Though such problems can be QMA-complete, our examples show that isotropic entanglement provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.     

Entropy growth and degradation of entanglement due to phase decoherence in ion traps

We study how phase decoherence through intrinsic decoherence leads to growing entropy and a strong degradation of the maximum generated entanglement as a measure of information content of ionic state due to ion-laser interaction with a trapped ion. We calculate the partial entropy of the particle (atom or trapped ion) and field subsystems as well as the total entropy. The total entropy is shown to increase with time. Thus, the partial field or atomic entropy cannot be used as a direct measure of the particle–field entanglement. We find that, at least qualitatively, the difference between the total entropy and the sum of field and atom partial entropies can be used as an entanglement measure, when compared with an established entanglement measure based on the negativity of the eigenvalues of the partially transposed density matrix. We find a very strong sensitivity of the maximum generated entanglement on the decoherence and the chosen intrinsic decoherence parameter.     

Initial conditions and entanglement sudden death

We report results bearing on the behavior of non-local decoherence and its potential for being managed or even controlled. The decoherence process known as entanglement sudden death (ESD) can drive prepared entanglement to zero at the same time that local coherences and fidelity remain non-zero. For a generic ESD-susceptible Bell superposition state, we provide rules restricting the occurrence and timing of ESD, amounting to management tools over a continuous variation of initial conditions. These depend on only three parameters: initial purity, entanglement and excitation. Knowledge or control of initial phases is not needed.     

Quantum random access memory

A random access memory (RAM) uses n bits to randomly address N=2(n) distinct memory cells. A quantum random access memory (QRAM) uses n qubits to address any quantum superposition of N memory cells. We present an architecture that exponentially reduces the requirements for a memory call: O(logN) switches need be thrown instead of the N used in conventional (classical or quantum) RAM designs. This yields a more robust QRAM algorithm, as it in general requires entanglement among exponentially less gates, and leads to an exponential decrease in the power needed for addressing. A quantum optical implementation is presented.