When Is a Genuine Multipartite Entanglement Measure Monogamous?

A crucial issue in quantum communication tasks is characterizing how quantum resources can be quantified and distributed over many parties. Consequently, entanglement has been explored extensively. However, there are few genuine multipartite entanglement measures and whether it is monogamous is so far unknown. In this work, we explore the complete monogamy of genuine multipartite entanglement measure (GMEM) for which, at first, we investigate a framework for unified/complete GMEM according to the unified/complete multipartite entanglement measure we proposed in 2020. We find a way of inducing unified/complete GMEM from any given unified/complete multipartite entanglement measure. It is shown that any unified GMEM is completely monogamous, and any complete GMEM that is induced by given complete multipartite entanglement measure is completely monogamous. In addition, the previous GMEMs are checked under this framework. It turns out that the genuinely multipartite concurrence is not as good of a candidate as GMEM.     

基于四波混频过程和线性分束器产生四组份纠缠

多组份纠缠是量子信息处理的重要资源,它的产生通常涉及到许多复杂的线性和非线性过程.本文从理论上提出了一种利用两个独立的四波混频过程和线性分束器产生真正的四组份纠缠的方案,其中,线性分束器的作用是将两个独立的四波混频过程联系起来.首先应用部分转置正定判据研究了强度增益对四组份纠缠的影响,结果表明,在整个增益区域内都存在真正的四组份纠缠,并且随着强度增益的增加,纠缠也在增强.然后研究了线性分束器的透射率对四组份纠缠的影响,发现只要线性分束器的透射率不为0或1,该系统也可以产生真正的四组份纠缠.最后,通过研究该系统可能存在的三组份纠缠和两组份纠缠来揭示该系统的纠缠结构.本文理论结果为实验上利用原子系综四波混频过程产生真正的四组份纠缠提供了可靠的方案.     

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源. 然而当量子系统与环境相互作用时, 会不可避免地产生消相干导致纠缠下降, 因此保护纠缠不受环境的影响具有重要意义. 振幅衰减是一种典型的衰减机制. 如果探测环境保证没有激发从系统中流出, 即视为对系统的一种弱测量. 本文基于局域脉冲序列和弱测量, 提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案, 保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和Maximal slice态.     

Entanglement Dynamics of Quantum States Undergoing Decoherence from a Driven Critical Environment

In this paper,we have investigated the quantum entanglement of quantum states undergoing decoherence from a spin environment which drives a quantum phase transition.From our analysis,we find that the entanglement dynamics depends not only on the coupling strength but also on the external magnetic field and the number of the freedom degrees of the environment.Specially,our results imply that the decay of the entanglement can be enhanced by the quantum phase transition of the environment when the system is coupled to the environment weakly.Additionally,the discussion of the case of the multipartite states with high dimensions is made.     

Entanglement Dynamics of Quantum States Undergoing Decoherence from a Driven Critical Environment

In this paper, we have investigated the quantum entanglement of quantum states undergoing decoherence from a spin environment which drives a quantum phase transition. From our analysis, we find that the entanglement dynamics depends not only on the coupling strength but also on the external magnetic field and the number of the freedom degrees of the environment. Specially, our results imply that the decay of the entanglement can be enhanced by the quantum phase transition of the environment when the system is coupled to the environment weakly. Additionally, the discussion of the case of the multipartite states with high dimensions is made.     

Decoherence of genuine multipartite entanglement for local non-Markovian–Lorentzian reservoirs

We study decoherence effects on genuine multipartite entanglement for three and four qubits, spatially separated and subjected to local Lorentzian reservoirs. Employing recent techniques to compute genuine negativity for multipartite systems and an exact solvable model, we analyze the dynamics of genuine entanglement for different coupling bandwidths and detunings. We find that collapses and revivals can occur by varying these parameters for various multipartite quantum states.     

Operational interpretation for global multipartite entanglement

We introduce an operational interpretation for pure-state global multipartite entanglement based on quantum estimation. We show that the estimation of the strength of low-noise locally depolarizing channels, as quantified by the regularized quantum Fisher information, is directly related to the Meyer-Wallach multipartite entanglement measure. Using channels that depolarize across different partitions, we obtain related multipartite entanglement measures. We show that this measure is the sum of expectation values of local observables on two copies of the state.     

Decoherence suppression for three-qubit W-like state using weak measurement and iteration method

Multi-qubit entanglement states are the key resources for various multipartite quantum communication tasks. For a class of generalized three-qubit quantum entanglement, W-like state, we demonstrate that the weak measurement and the reversal measurement are capable of suppressing the amplitude damping decoherence by reducing the initial damping factor into a smaller equivalent damping factor. Furthermore, we propose an iteration method in the weak measurement and the reversal measurement to enhance the success probability of the total measurements. Finally, we discuss how the number of the iterations influences the overall effect of decoherence suppression, and find that the "half iteration" method is a better option that has more practical value.     

Construction of Complete Orthogonal Genuine Multipartite Entanglement State

With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement(GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a 3-order 3-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.     

Entanglement in four qubit states: Polynomial invariant of degree 2, genuine multipartite concurrence and one-tangle

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.     

Enhancing robustness of multiparty quantum correlations using weak measurement

Multipartite quantum correlations are important resources for the development of quantum information and computation protocols. However, the resourcefulness of multipartite quantum correlations in practical settings is limited by its fragility under decoherence due to environmental interactions. Though there exist protocols to protect bipartite entanglement under decoherence, the implementation of such protocols for multipartite quantum correlations has not been sufficiently explored. Here, we study the effect of local amplitude damping channel on the generalized Greenberger–Horne–Zeilinger state, and use a protocol of optimal reversal quantum weak measurement to protect the multipartite quantum correlations. We observe that the weak measurement reversal protocol enhances the robustness of multipartite quantum correlations. Further it increases the critical damping value that corresponds to entanglement sudden death. To emphasize the efficacy of the technique in protection of multipartite quantum correlation, we investigate two proximately related quantum communication tasks, namely, quantum teleportation in a one sender, many receivers setting and multiparty quantum information splitting, through a local amplitude damping channel. We observe an increase in the average fidelity of both the quantum communication tasks under the weak measurement reversal protocol. The method may prove beneficial, for combating external interactions, in other quantum information tasks using multipartite resources.     

Schmidt Number Entanglement Measure for Multipartite k-nonseparable States

In this paper, an entanglement measure for multipartite quantum states with respect to k-partition was introduced, which is called Schmidt number entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k-ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states.

     

Constructing unextendible product bases from multiqubit ones

The construction of multipartite unextendible product bases(UPBs) is a basic problem in quantum information.We respectively construct two families of 2 × 2× 4 and 2 × 2 × 2 × 4 UPBs of size eight by using the existing four-qubit and five-qubit UPBs.As an application,we construct novel families of multipartite positive-partial-transpose entangled states,as well as their entanglement properties in terms of the geometric measure of entanglement.     

Enlarged omnidirectional photonic gap in one dimensional ternary plasma photonic crystals that contain metamaterials

We study the dynamics of multipartite quantum correlations measured by the lower bound of concurrence and quantum discord in a three-qubit system coupled to an XY spin chain. For the initial pure GHZ and W state, we find the lower bound of entanglement is more robust than the quantum discord against the decoherence induced by the spin environment. But for the Werner state, the sudden death of discord is not observed even in the presence of entanglement sudden death. By comparing the evolutions for the GHZ and W states, we show that the W state preserves more quantum correlations than the GHZ state. In addition, we put research emphasis on the relation between the dynamics of multipartite quantum correlations and the quantum phase transition of the spin environment.     

A Reversible Theory of Entanglement and its Relation to the Second Law

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein’s Lemma, giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.     

利用非简并光学参量振荡腔产生连续变量三色三组分纠缠态

利用半经典理论方法计算了运转于阈值以上的非简并光学参量振荡腔输出信号场、闲置场及反射抽运场的关联特性. 根据 van Loock 等提出的连续变量多组分纠缠判据, 计算结果表明, 常温下这三个光场的正交振幅分量与正交位相分量之间存在三组分量子关联, 得到了三色三组分纠缠态光场. 数值计算了关联噪声对参量振荡腔物理参数的依赖关系, 找出了产生三色三组分纠缠态产生的最佳运转条件, 为连续变量多组分纠缠态光场产生系统的设计提供了直接参考. 关键词： 连续变量 非简并光学参量振荡腔 三色三组分纠缠态     

Dynamics of genuine multipartite entanglement under local non-Markovian dephasing

We study dynamics of genuine entanglement for quantum states of three and four qubits under non-Markovian dephasing. Using a computable entanglement monotone for multipartite systems, we find that the GHZ state is quite resilient state whereas the W state is the most fragile. We compare dynamics of chosen quantum states with dynamics of random pure states and weighted graph states.     

Entanglement Dynamics of the Double Intensity-Dependent Coupling Jaynes-Cummings Models

We consider entanglement dynamics of double intensity-dependent coupling Jaynes-Cummings models with two different initial light fields, which one is in the squeezed vacuum state and another is in the coherent state. The results show that, when the compressibility factor and the mean photon number are smaller, the concurrence of atoms exhibits phenomenon of dead and revival periodically, and the entanglement perfectly transferres between the atoms and the fields. As the value of them grow larger, the entanglement sudden death and sudden revival come out. Comparing with the normal double Jaynes-Cummings model, we notice that the concurrence of the atoms which in the normal double Jaynes-Cummings models evolves irregularly. And it is find that periodical entanglement pulse can be generated by using double intensity-dependent coupling Jaynes-Cummings models. This result might be useful in quantum information processes.     

Verifying genuine high-order entanglement

High-order entanglement embedded in multipartite multilevel quantum systems (qudits) with many degrees of freedom (DOFs) plays an important role in quantum foundation and quantum engineering. Verifying high-order entanglement without the restriction of system complexity is a critical need in any experiments on general entanglement. Here, we introduce a scheme to efficiently detect genuine high-order entanglement, such as states close to genuine qudit Bell, Greenberger-Horne-Zeilinger, and cluster states as well as multilevel multi-DOF hyperentanglement. All of them can be identified with two local measurement settings per DOF regardless of the qudit or DOF number. The proposed verifications together with further utilities such as fidelity estimation could pave the way for experiments by reducing dramatically the measurement overhead.     

Detecting entanglement of quantum channels

Entanglement is the crucial resource for different quantum information processing tasks. While conventional studies focus on the entanglement of bipartite or multipartite quantum states, recent works have extended the scenario to the entanglement of quantum channels, an operational quantification of the channel entanglement manipulation capability. Based on the recently proposed channel entanglement resource framework, here we study a further task of resource detection—witnessing entanglement of quantum channels. We first introduce the general framework and show how channel entanglement detection is related to the Choi state of the channel, enabling channel entanglement detection via conventional state entanglement detection methods. We also consider entanglement of multipartite quantum channels and use the stabilizer formalism to construct entanglement witnesses for circuits consisting of controlled-Z gates. We study the effectiveness of the proposed detection methods and compare their performance for several typical channels. Our work paves the way for systematic theoretical studies of channel entanglement and practical benchmarking of noisy intermediate scaled quantum devices.