Geometric Phases for Mixed States in Trapped Ions

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover, special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.     

Geometric Phases for Mixed States in Trapped Ions

The generalization of geometric phase from the pure states to the mixed states may have potential applications in constructing geometric quantum gates. We here investigate the mixed state geometric phases and visibilities of the trapped ion system in both non-degenerate and degenerate cases. In the proposed quantum system, the geometric phases are determined by the evolution time, the initial states of trapped ions, and the initial states of photons. Moreover,special periods are gained under which the geometric phases do not change with the initial states changing of photon parts in both non-degenerate and degenerate cases. The high detection efficiency in the ion trap system implies that the mixed state geometric phases proposed here can be easily tested.     

二非正交纯态相混合的concurrence

导出了两量子比特中二非正交纯态相混合的concurrence 的明显表达式, 并作了验证. 推算表明，正交情形下的concurrence公式可以直接推广到非正交的情形. 讨论了两纯态相混合的最大纠缠混合态和一些重要特殊情形. 关键词： 量子纠缠 纯态 混合态 concurrence     

Entanglement and Pancharatnam Phase for Two Two-Level Atoms Interacting with a Single Mode Field

A model of two 2-level atoms interacts with a single quantized electromagnetic field is considered. We study the effect of the mean photon number and the structure of the initial states of the two atoms on the dynamics of the atomic system from the separability point of view. It is found that, if we start from a product mixed atomic state, the probability of generating long living entangled states is increased as the mean photon number increases. Starting from excited atomic system in product state, one generates a more stable entangled states with high degree of entanglement. Also, the effect of the mean photon number on atomic system prepared initially in entangled states is investigated. It is found that the entangled state generated from the initially partial entangled states are more robust than those obtained from a maximum entangled state. The Pancharatnam phase for the separable and entangled states is studied under the effect of the mean photon number and the structure of the initial state. We find that for the separable states, the collapses decrease and the amplitude of the revivals is smaller than that for the entangled state, so there are long-living entangled phases. This property give us a great chances to store safely information in entangled state.     

Ground state phase diagram of the infinite dimensional Hubbard model: A variational study

We use the Gutzwiller variational method to study the ground state phase diagram of the infinite dimensional Hubbard model, paying special attention to features associated with the Gaussian form of the tight binding band density of states. We only consider trial states for which the validity of the Gutzwiller approximation has been proven, i.e., the paramagnetic, ferromagnetic, and two-sublattice antiferromagnetic states. We map out the phase diagram numerically, and give approximate analytic arguments to explain the behaviour in the small-U, and large-U limits. We give two versions of the phase diagram: one restricted to homogeneous phases, and another when phase separation is allowed. In the latter case, a homogeneous antiferromagnetic state is found only at exact half-filling, where the state is also insulating. Off half-filling, four different regions are found: pure paramagnetic, and ferromagnetic states, as well as antiferromagnetic-paramagnetic, and antiferromagnetic-ferromagnetic mixed phases.Dedicated to Professor W. Brenig on the occasion of his 60th birthdayResearch performed within the program of the Sonderforschungsbereich 341 supported by the Deutsche Forschungsgemeinschaft     

Catalysis of entanglement manipulation for mixed states

We consider entanglement-assisted remote quantum state manipulation of bipartite mixed states. Several aspects are addressed: we present a class of mixed states of rank two that can be transformed into another class of mixed states under entanglement-assisted local operations with classical communication, but for which such a transformation is impossible without assistance. Furthermore, we demonstrate enhancement of the efficiency of purification protocols with the help of entanglement-assisted operations. Finally, transformations from one mixed state to mixed target states which are sufficiently close to the source state are contrasted with similar transformations in the pure-state case.     

非均匀磁场中的海森堡XY模型热纠缠信道的量子隐形传送

在量子通讯的实验中,由于外界环境的影响,我们很难得到最大的纠缠纯态.量子信道可能以混合纠缠态的形式出现.而固体材料中的热平衡态就是一种重要的混合纠缠态.本文利用了两个独立的外加不均匀磁场的一维海森堡链的热纠缠态作为量子信道,实现了两粒子纠缠态的远程传送,分析了外界温度和磁场对纠缠和传输保真度的影响.为了突出传输效果,我们对平均保真度做了研究,结果发现当温度很低,外加反方向的磁场B1和B2时,平均保真度大于经典通道的传输极限值2/3.     

Self-entanglement and the dissociation of homonuclear diatomic molecules

The concept of self-entanglement is introduced to describe a mixed state or ensemble density as a pure state in an augmented Hilbert space formed by the products of the individual states forming a mixed state (or ensemble). We use this representation of mixed states to show that upon dissociation a neutral homonuclear diatomic molecule will separate into two neutral atoms.     

类氢原子核质量对电子状态的影响

在孤立的两体复合系统中,讨论其中一体的变化如何影响另一体的状态,有助于了解单粒子混合态与纯态的关系.本文讨论5个孤立的一维类氢原子模型系统,原子核的质量互不相同.这5个两体(电子与原子核)复合系统的相对运动状态都处于纠缠态,其中电子状态都用约化密度矩阵表示的混合态描述.在原子核质量趋近无穷大的一维氢原子模型中,电子处于纯态.为比较这里的纯态和混合态,在位置表象中计算了这些混合态的纯度、它们分别与纯态的保真度、以及所有这些态的相干性.研究表明,原子核的质量越大,纯度和保真度越接近1,混合态的相干性与纯态的也越接近.这样的纯态及其相干性可以是这种混合态及其相干性的近似,并与原子核及库仑相互作用有关.     

Quantum speed limit for mixed states in a unitary system

Since the evolution of a mixed state in a unitary system is equivalent to the joint evolution of the eigenvectors contained in it, we could use the tool of instantaneous angular velocity for pure states to study the quantum speed limit (QSL) of a mixed state. We derive a lower bound for the evolution time of a mixed state to a target state in a unitary system, which automatically reduces to the quantum speed limit induced by the Fubini-Study metric for pure states. The computation of the QSL of a degenerate mixed state is more complicated than that of a non-degenerate mixed state, where we have to make a singular value decomposition (SVD) on the inner product between the two eigenvector matrices of the initial and target states. By combing these results, a lower bound for the evolution time of a general mixed state is presented. In order to compare the tightness among the lower bound proposed here and lower bounds reported in the references, two examples in a single-qubit system and in a single-qutrit system are studied analytically and numerically, respectively. All conclusions derived in this work are independent of the eigenvalues of the mixed state, which is in accord with the evolution properties of a quantum unitary system.     

Quantum Entanglement Swapping in a Non-Markovian Environment

We propose an entanglement swapping scheme for mixed states in a classical non-Markovian noises, which is modelled as the so-called Ornstein-Uhlenbeck processes. The two mixed states before entanglement swapping are two X-type mixed states, which are caused by the environment-induced decoherence on the initially Bell states. This is more practical than the pure state case in quantum information processing. The fidelity and concurrence of the post-swapping states are discussed.     

Scheme for purifying a general mixed entangled state and its linear optical implementation

We propose a scheme for purification of a general mixed entangled state. In this scheme, we start from a large number of general mixed entangled states and end up, after local operation and classical communication, with a smaller number of Bell diagonal states with higher entanglement. In particular, the scheme can purify one maximally entangled state from two entangled pairs prepared in a class of mixed entangled state. Furthermore we propose a linear optical implementation of the present scheme with polarization beam splitters and photon detectors.     

Increasing of population trapping and transferring in a modified laser-induced continuum structure system by phase control

The atomic coherent population trapping in the system of an atom with one ground state, a pair of excited states and a set of continuum states, interacting with two temporally separated sets of laser pulses with different phases is investigated. The relative phases of laser pulses on the amount of atomic populations trapped in the three bound states and the efficiency of population transfer are analyzed.     

Fidelity between Gaussian mixed states with quantum state quadrature variances

In this paper, from the original definition of fidelity in a pure state, we first give a well-defined expansion fidelity between two Gaussian mixed states. It is related to the variances of output and input states in quantum information processing. It is convenient to quantify the quantum teleportation(quantum clone) experiment since the variances of the input(output) state are measurable. Furthermore, we also give a conclusion that the fidelity of a pure input state is smaller than the fidelity of a mixed input state in the same quantum information processing.     

GEOMETRIC PHASES AND SCHR?DINGER''S CAT STATE

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr?dinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.     

Entanglement Dynamics of Two Qubits Coupled to a Noise Environment

We study the time evolution of two two-state systems （two qubits） initially in the pure entangled states or the maximally entangled mixed states interacting with the individual environmental noise. It is shown that due to environment noise, all quantum entangled states are very fragile and become a classical mixed state in a short-time limit. But the environment can affect entanglement in very different ways. The type of decoherence process for certain entangled states belongs to amplitude damping, while the others belong to dephasing decoherenee.     

GEOMETRIC PHASES AND SCHR?DINGER'S CAT STATE

A matrix method is presented for treating the dynamical phases, adiabatic phases and nonadiabatic phases of quantum superposition states. It is effective for any parameter-varying Hamiltonian system. As two examples, the evolution of mass-varying harmonic oscillator and the evolution of coherent states under parameter-varying displaced operator have been studied, Some new phenomena are obtained in the first case and the possible producing of so-called Schr?dinger's cat state by geometric phases is pointed out. The quantum state useful for the quantum optical verification of Berry's phase is introduced.     

Optimal Purification of Arbitrary Quantum Mixed States

The quantum state purification is very important in quantum information processing. Our purpose is to purify arbitrary mixed state into some pure state. We present one simple method to purify arbitrary mixed state from its normal Schmidt decomposition. This scheme is also simplified by using only two special unitary transformations, and can be used to prove the typical entanglement thresholds for random mixed states.     

Mixtures of maximally entangled pure states

We study the conditions when mixtures of maximally entangled pure states remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to ensure that the resulting mixed state is genuinely entangled. Also, we demonstrate how these results could be applied as a way to detect entanglement in mixtures of the entangled pure states with noise.