Test of Inseparability Criteria for Squeezed Number States of the Radiation Field

We investigate the efficiency of inseparability criteria in detecting the entanglement properties of two-mode non-Gaussian states of the electromagnetic field. We focus our study on the relevant class of two-mode squeezed number states. These states combine the entangling capability of two-mode squeezers with the non-Gaussian character (nonclassicality) of number states. They allow for some exact analytical treatments, and include as a particular case the two-mode Gaussian squeezed vacuum. We show that the generalized PPT criterion recently proposed by Shchukin and Vogel, based on higher order statistical moments, is very efficient in detecting the entanglement for this class of non-Gaussian states.     

Nonlinear entanglement witnesses based on continuous-variable local orthogonal observables for bipartite systems

In this paper, a nonlinear entanglement witness criterion based on continuous-variable local orthogonal observables for bipartite states is established, which is strictly stronger than the the linear entanglement witnesses criterion introduced by Zhang et al. (Phys. Rev. Lett. 111:190501, 2013). This criterion is particularly applied to two-mode Gaussian states yielding a criterion in terms of the covariance matrix. Comparison with CCNR criterion is discussed.     

Further Results on the Cross Norm Criterion for Separability

In the present paper we develop and investigate a novel approach that aims to characterize quantum entanglement by using cross norms. In the first part of the paper we further develop the mathematical theory by determining the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the second part we show that our techniques induce a novel powerful analytical and computable separability criterion for bipartite systems. This new criterion complements the well-known Peres positive partial transpose criterion in several aspects. It is a necessary but in general not a sufficient criterion for separability. We demonstrate the power of the new criterion by evaluating the criterion for a number of important examples. We also demonstrate that the new criterion is able to detect bound entangled states.     

Spin Squeezing Criterion with Local Unitary Invariance

We propose a spin squeezing criterion for arbitrary multi-qubit states that is invariant under local unitary operations. We find that, for arbitrary pure two-qubit states, spin squeezing is equivalent to entanglement, and multi-qubit states are entangled if this new spin squeezing parameter is less than unity. PACS: 03.67.-a; 03.65.Ud     

Dzyaloshinskii–Moriya interaction as an agent to free the bound entangled states

In the present paper, we investigate the efficacy of Dzyaloshinskii–Moriya (DM) interaction to convert the bound entangled states into free entangled states. We consider the tripartite hybrid system as a pair of non interacting two qutrits initially prepared in bound entangled states and one auxiliary qubit. Here, we consider two types of bound entangled states investigated by Horodecki. The auxiliary qubit interacts with any one of the qutrit of the pair through DM interaction. We show that by tuning the probability amplitude of auxiliary qubit and DM interaction strength, one can free the bound entangled states, which can be further distilled. We use the reduction criterion to find the range of the parameters of probability amplitude of auxiliary qubit and DM interaction strength, for which the states are distillable. The realignment criterion and negativity have been used for detection and quantification of entanglement.     

Disentanglement and quantum states transitions dynamics in spin-qutrit systems: dephasing random telegraph noise and the relevance of the initial state

Using negativity and realignment criterion as quantifiers of free and bound entanglements respectively, we present in details the analytical study of the entanglements and quantum states transitions dynamics in a two-qutrit system driven by dephasing random telegraph noise channel(s). Both collective and independent system–environment couplings as well as the Markovian and the non-Markovian regimes of the noise channel(s) are considered. Two non-equivalent initial states and their locally equivalent through a local unitary operation (LUO) are also considered. We demonstrate a stronger entanglement under independent Markovian environments than with a collective one; meanwhile, for the non-Markovian regime, entanglement is stronger under a collective environment than with independent ones. States transitions as well as the (re)activation of bound entanglement (for initially free entangled states) can be found for a specific class of initial states, but can, however, be avoided by means of a LUO on the initial state. While unavoidable disentanglement occurs for independents coupling, we demonstrate the possibility of indefinite free entanglement survival in the qutrit system under a common environment by converting the initial entangled state using the local unitary operation.     

非高斯环境下基于信息熵准则的定点平滑估计算法

针对一类非高斯噪声环境下固定点平滑估计问题,设计一种使用最大相关熵准则作为最优估计标准的平滑估计算法,称之为固定点最大相关熵平滑估计(fixed-point maximum correntropy smoother,FP-MCS).首先基于矩阵变换给出最大相关熵Kalman滤波的新表达形式;然后以此为基础,引入新的状态来扩展系统,并推导出固定点最大相关熵平滑估计的在线迭代方程;进一步比较平滑前后状态估计误差协方差,从理论上分析算法的性能改进,同时比较其计算复杂度;最后通过算例验证所设计的算法在非高斯混合噪声干扰下的有效性和优越性.     

Tight bounds for the eavesdropping collective attacks on general CV-QKD protocols that involve non-maximally entanglement

A new method to quantify the eavesdropper’s accessible information on continuous variable quantum key distribution for protocols implementing homodyne and heterodyne detections is introduced. We have derived upper bounds for the eavesdropping collective attacks on general continuous variable quantum key distribution protocols. Our focus is especially on deriving bounds which are Gaussian optimal for Eve collective attacks that involve non maximally entanglement (i.e. Alice and Bob use non maximally entangled states or non-Gaussian modulation for their quantum key distribution protocols). The new bounds derived are tight for all continuous variable quantum key distribution protocols. We show that the eavesdropper’s accessible information is independent of the initial correlation between Alice and Bob modes in reverse reconciliation scheme, while in direct reconciliation scheme, Eve information is given as a function of Alice and Bob initial correlation.     

Entanglement measure for pure six-qubit quantum states

In this work we propose a six-way entanglement measure for pure six-qubit quantum states. The proposed measure is used to quantify the entanglement of some six-qubit states useful in quantum information processing and in the analysis of entanglement variation of some parameterized six-qubit states.     

Generation and entanglement of multi-dimensional multi-mode coherent fields in cavity QED

We introduce generalized multi-mode superposition of multi-dimensional coherent field states and propose a generation scheme of such states in a cavity QED scenario. An appropriate encoding of information on these states is employed, which maps the states to the Hilbert space of some multi-qudit states. The entanglement of these states is characterized based on such proper encodings. A detailed study of entanglement in general multi-qudit coherent states is presented, and in addition to establishing some explicit expressions for quantifying entanglement of such systems, several important features of entanglement in these system states are exposed. Furthermore, the effects of both cavity decay and channel noise on these system states are studied and their properties are illustrated.     

Residual entanglement with negativity for pure four-qubit quantum states

In this work we study the entanglement of pure four-qubit quantum states. The analysis is realized, firstly, through the comparison between two different entanglement measures: the Groverian entanglement measure and the residual entanglement calculated with negativities. After, we use the last to measure the entanglement of several four-qubit states and the variation of the entanglement when the four-qubit state is processed by a two-qubit gate.     

A new method for quantifying entanglement of multipartite entangled states

We propose a new way for quantifying entanglement of multipartite entangled states which have a symmetrical structure and can be expressed as valence-bond-solid states. We put forward a new concept ‘unit.’ The entangled state can be decomposed into a series of units or be reconstructed by multiplying the units successively, which simplifies the analyses of multipartite entanglement greatly. We compute and add up the generalized concurrence of each unit to quantify the entanglement of the whole state. We verify that the new method coincides with concurrence for two-partite pure states. We prove that the new method is a good entanglement measure obeying the three necessary conditions for all good entanglement quantification methods. Based on the method, we compute the entanglement of multipartite GHZ, cluster and AKLT states.     

Quantum correlations in Gaussian states via Gaussian channels: steering,entanglement, and discord

Here we study the quantum steering, quantum entanglement, and quantum discord for Gaussian Einstein–Podolsky–Rosen states via Gaussian channels. And the sudden death phenomena for Gaussian steering and Gaussian entanglement are theoretically observed. We find that some Gaussian states have only one-way steering, which confirms the asymmetry of quantum steering. Also we investigate that the entangled Gaussian states without Gaussian steering and correlated Gaussian states own no Gaussian entanglement. Meanwhile, our results support the assumption that quantum entanglement is intermediate between quantum discord and quantum steering. Furthermore, we give experimental recipes for preparing quantum states with desired types of quantum correlations.     

Asymptotic entanglement in quantum walks from delocalized initial states

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.     

Study of a monogamous entanglement measure for three-qubit quantum systems

The entanglement quantification and classification of multipartite quantum states is an important research area in quantum information. In this paper, in terms of the reduced density matrices corresponding to all possible partitions of the entire system, a bounded entanglement measure is constructed for arbitrary-dimensional multipartite quantum states. In particular, for three-qubit quantum systems, we prove that our entanglement measure satisfies the relation of monogamy. Furthermore, we present a necessary condition for characterizing maximally entangled states using our entanglement measure.     

Entanglement dynamics in two-parameter qubit–qutrit states under Dzyaloshinskii–Moriya interaction

We study entanglement dynamics in two-parameter qubit–qutrit states under the influence of Dzyaloshisnhkii–Moriya (DM) interaction. Our system consists of a qubit–qutrit pair as a closed system initially in two-parameter class of states, and one environmental qubit interacts with the qutrit of the closed system via DM interaction. We divide our analysis into two cases. In the first case, we study the entanglement dynamics in separable region, and in the second case we study the same in non-separable region. The DM interaction produces the entanglement in separable region with entanglement sudden death (ESD) and some states in this region remain unaffected by the same. In non-separable region, all the states are affected by DM interaction. The DM interaction excites the entanglement but does not produce ESD in this region. We observed that probability amplitude of environmental qubit does not affect the entanglement in two-parameter qubit–qutrit states in both the regions.     

Separability of Mixed Quantum States: Linear Contractions and Permutation Criteria

Recently, a powerful separability criterion was introduced by O. Rudolf in [5] and by K. Chen et al. in [6] – basing on realignment of elements of density matrix. Composing the main idea behind the above criterion and the necessary and sufficient condition in terms of positive maps, we provide a characterization of separable states by means of linear contractions. The latter need not be positive maps. We extend the idea to multipartite systems, and find that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely tri-parite entanglement. We generalize it by introducing a family of so called permutation separability criteria for multipartite states. Namely, any permutation of indices of density matrix written in product basis leads to a separability criterion. Partial transpose and realignment criterion are special cases of permutation criteria. An early version of the present paper has appeared in e-print archive as quant-ph/0206008. The premutation criterion has been then further developed in [23, 24, 25], where the problem of classification of inequivalent permutation criteria has been investigated.     

Protecting quantum entanglement and correlation by local filtering operations

In this work, the protection of different quantum entanglement and correlation is explored by local filtering operations. The results show that the filtering operations can indeed be useful for combating amplitude-damping decoherence and recovering the quantum entanglement and correlation. In this scheme, although the final states satisfy the quantum entanglement and correlation, the corresponding initial noisy states does not satisfy them, which means that the filtering operations can reveal the hidden genuine quantum entanglement and correlation of these initial noisy states.     

Exploring degrees of entanglement

In spite of a long history, the quantification of entanglement still calls for exploration. What matters about entanglement depends on the situation, and so presumably do the numbers suitable for its quantification. Regardless of situational complications, a necessary first step is to make available for calculation some quantitative measure of entanglement. Here we define a geometric degree of entanglement, distinct from earlier definitions, but in the case of bipartite pure states related to that proposed by Shimony (Ann N Y Acad Sci 755:675–679, 1995). The definition offered here applies also to multipartite mixed states, and a variational method simplifies the calculation. We analyze especially states that are invariant under permutation of particles, states that we call bosonic. Of interest to quantum sensing, for bosonic states, we show that no partial trace can increase a degree of entanglement. For some sample cases we quantify the degree of entanglement surviving a partial trace. As a function of the degree of entanglement of a bosonic 3-qubit pure state, we show the range of degree of entanglement for the 2-qubit reduced density matrix obtained from it by a partial trace. Then we calculate an upper bound on the degree of entanglement of the mixed state obtained as a partial trace over one qubit of a 4-qubit bosonic state. As a reminder of the situational dependence of the advantage of entanglement, we review the way in which entanglement combines with scattering theory in the example of light-based radar.     

Entanglement detection and distillation for arbitrary bipartite systems

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability.