Geometric discord of tripartite quantum systems

We study the quantification of geometric discord for tripartite quantum systems.Firstly,we obtain the analytic formula of geometric discord for tripartite pure states.It is already known that the geometric discord of pure states reduces to the geometric entanglement in bipartite systems,the results presented here show that this property is no longer true in tripartite systems.Furthermore,we provide an operational meaning for tripartite geometric discord by linking it to quantum state discrimination,that is,we prove that the geometric discord of tripartite states is equal to the minimum error probability to discriminate a set of quantum states with von Neumann measurement.Lastly,we calculate the geometric discord of three-qubit Bell diagonal states and then investigate the dynamic behavior of tripartite geometric discord under local decoherence.It is interesting that the frozen phenomenon exists for geometric discord in this scenario.

Geometric quantum discord and Berry phase between two charge qubits coupled by a quantum transmission line

Geometric quantum discord（GQD） and Berry phase between two charge qubits coupled by a quantum transmission line are investigated. We show how GQDs evolve and investigate their dependencies on the parameters of the system.We also calculate the energy and the Berry phase and compare them with GQD, finding that there are close connections between them.

Geometrical quantum discord and negativity of two separable and mixed qubits

We studied quantum correlation and quantum entanglement of a quantum system in which a coherent state light field interacts with two qubits that are initially prepared in a separable and mixed state.The influence of mean photon number of the coherent field and distribution probability of the atom on the geometrical quantum discord and the negativity are discussed.Our results show that the mean photon number of light field and distribution function of the atom can regulate and control the quantum correlation and quantum entanglement.

Protecting geometric quantum discord via partially collapsing measurements of two qubits in multiple bosonic reservoirs

We study the dynamics of geometric quantum discord(GQD) between two qubits,each qubit interacting at the same time with K independent multiple bosonic reservoirs at zero temperature.In both weak and strong qubit-reservoirs coupling regimes,we find that the increase of the number K of reservoirs can induce the damped oscillation of GQD,and enhance the memory effects of the overall environment.And the Hilbert-Schmidt norm GQD(two-norm GQD) is always smaller than the trace norm geometric quantum discord(one-norm GQD).Therefore,the one-norm GQD is a better way to measure the quantum correlation.Finally,we propose an effective strategy to improve GQD by using partially collapsing measurements,and we find that the protection effect is better with the increase of the weak measurement strength.

Geometric global quantum discord of two-qubit states

We consider the geometric global quantum discord （GGQD） of two-qubit systems. By analyzing the symmetry of geometric global quantum discord we give an approach for deriving analytical formulae of the extremum problem which lies at the core of computing the GGQD for arbitrary two-qubit states. Furthermore, formulae of GGQD of arbitrary two-qubit states and some concrete examples are presented.

Super Quantum Discord and Inferior “Geometric Discord” Based on Weak Measurement in Noninertial Frames

Instead of projective measurement, we use weak measurement to define quantum and geometric discords, and compare them with the normal quantum and geometric discords based on the projective measurement in noninertial frames. We find that using weak measurement to define quantum discord we can capture more quantum correlations compared with the projective measurement, so calling it super quantum discord. However, we note that the geometric discord based on the weak measurements becomes smaller, so we name it inferior “geometric discord”. We also show that, although both the super quantum discord and the inferior “geometric discord” decrease with the increase of observer’s acceleration, the super quantum discord/inferior “geometric discord” increases/decreases as the measurements become weak. These differences reveal that the definitions of the quantum and geometric discords are not too concordant with each other.

Measurement-Induced Nonlocality and Geometric Discord in the Spin-Boson Model

Dynamics of measurement-induced-nonlocality (MIN) and geometric measure of discord (GD) in the spin-boson model is studied. Analytical results show that for two large classes of initial states, MINs are equal but GDs are different. At the end of evolution, MIN and GD initially stored in the spin system transfer completely to reservoirs. The quantum beats for MIN and GD are also found which are the results of quantum interference between two local non-Markovian dynamics via quantum correlation.

一类三量子比特X态的几何量子失协

基于[Phys Rev Lett,124,110401(2020)]中提出的多体量子失协的定义,该文通过测量诱导给出了依赖于四个实参数的一类三量子比特X态的几何量子失协解析表达式,并给出了该类态几何量子失协的等高图.作为应用,该文研究了相位翻转信道下三量子比特X态几何量子失协的动力学行为.

Research on the Freezing Phenomenon of Quantum Correlation by Machine Learning

Quantum correlation shows a fascinating nature of quantum mechanics and plays an important role in some physics topics,especially in the field of quantum information.Quantum correlations of the composite system can be quantified by resorting to geometric or entropy methods,and all these quantification methods exhibit the peculiar freezing phenomenon.The challenge is to find the characteristics of the quantum states that generate the freezing phenomenon,rather than only study the conditions which generate this phenomenon under a certain quantum system.In essence,this is a classification problem.Machine learning has become an effective method for researchers to study classification and feature generation.In this work,we prove that the machine learning can solve the problem of X form quantum states,which is a problem of physical significance.Subsequently,we apply the density-based spatial clustering of applications with noise(DBSCAN)algorithm and the decision tree to divide quantum states into two different groups.Our goal is to classify the quantum correlations of quantum states into two classes:one is the quantum correlation with freezing phenomenon for both Rènyi discord(α=2)and the geometric discord(Bures distance),the other is the quantum correlation of non-freezing phenomenon.The results demonstrate that the machine learning method has reasonable performance in quantum correlation research.

Monogamy of quantum correlations in the one-dimensional anisotropic XXXYYY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with stag- gered Dzyaloshinskii-Moriya （DM） interaction have been investigated using the quantum renormalization group （QRG） method. We summarize the monogamy relation for different quantum correlation measures and make an explicit compar- ison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.

Quantum correlation switches for dipole arrays

We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord （QD）, geometric measure of quantum discord （GMQD）, and measurement-induced disturbance （MID）, in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole-dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.

Geometric measure of quantum discord and the geometry of a class of two-qubit states

We investigate the geometric picture of the level surfaces of quantum entanglement and geometric measure of quantum discord(GMQD) of a class of X-states, respectively. This pictorial approach provides us a direct understanding of the structure of entanglement and GMQD. The dynamic evolution of GMQD under two typical kinds of quantum decoherence channels is also investigated. It is shown that there exists a class of initial states for which the GMQD is not destroyed by decoherence in a finite time interval. Furthermore, we establish a factorization law between the initial and final GMQD, which allows us to infer the evolution of entanglement under the influences of the environment.

quantum discord geometric measure quantum phase transition

A generalization of the geometric measure of quantum discord is introduced in this article, based on Hellinger distance. Our definition has virtues of computability and independence of local measurement. In addition it also does not suffer from the recently raised critiques about quantum discord. The exact result can be obtained for bipartite pure states with arbitrary levels, which is completely determined by the Schmidt decomposition. For bipartite mixed states the exact result can also be found for a special case. Furthermore the generalization into multipartite case is direct. It is shown that it can be evaluated exactly when the measured state is invariant under permutation or translation. In addition the detection of quantum phase transition is also discussed for Lipkin–Meshkov–Glick and Dicke model.

Genuine tripartite entanglement and geometric quantum discord in entangled three-body Unruh-DeWitt detector system

We studied the quantum correlations of a three-body Unruh-DeWitt detector system using genuine tripartite entanglement(GTE)and geometric quantum discord(GQD).We considered two representative three-body initial entangled states,namely the GHZ state and the W state.We demonstrated that the quantum correlations of the tripartite system are completely destroyed at the limit of infinite acceleration.In particular,it is found that the GQD of the two initial states exhibits“sudden change”behavior with increasing acceleration.It is shown that the quantum correlations of the W state are more sensitive than those of the GHZ state under the effect of Unruh thermal noise.The GQD is a more robust quantum resource than the GTE,and we can achieve robustness in discord-type quantum correlations by selecting the smaller energy gap in the detector.These findings provide guidance for selecting appropriate quantum states and resources for quantum information processing tasks in a relativistic setting.

基于腔QED系统的几何量子失谐及其传送（英文）

研究了基于腔量子电动力学(腔QED)系统的几何量子失谐及其传送.该系统包括两个独立的子系统,每个子系统由两个二能级原子与单模腔共振相互作用.结果表明,所有初始存储在原子A_1A_2中的几何量子失谐最终被转移到原子B_1B_2和腔C_1C_2.同时,原子A_1A_2,B_1B_2和腔C_1C_2的几何量子失谐在该量子系统中可以发生猝死(DSD)以及纠缠突然死亡(ESD).但是,在该量子系统中几何量子失谐不能完全由于原子的自发辐射和腔衰减而复活.此外,原子A_1A_2,B_1B_2和腔C_1C_2几何量子失谐的量,取决于其纯度p,并与其成比例,p的值越小,几何失谐越小.它也表明,在原子自发辐射和腔衰减的情况下,原子A_1A_2,B_1B_2和腔C_1C_2的几何量子失谐将经历振荡衰减并最终衰减到零.不过,在没有原子自发辐射和腔衰减的情况下,原子A_1A_2,B_1B_2和腔C_1C_2的几何量子失谐却没有衰减.

超导电荷量子比特系统中几何量子失协和稠密编码

研究了由约瑟夫森结耦合的两个超导电荷量子比特模型中的几何量子失协和稠密编码信道容量。讨论了初始平均光子数、相对相位和两电荷量子比特间振幅对几何量子失协和稠密编码信道容量的影响。结果表明,初始平均光子数、相对相位和两电荷量子比特间振幅在几何量子失协及稠密编码信道容量的动力学演化过程中扮演了一个非常重要的角色,特别有意义的是可以通过调控相对相位来提高稠密编码信道容量的值。

单Jaynes-Cummings原子与孤立原子系统中的各种量子关联

利用单Jaynes-Cummings(J-C)二能级原子和孤立原子构成的模型,研究了该模型中的各种量子关联。基于Dakic等提出的几何量子失协的度量方法,采用数值计算方法分析了系统中两原子间几何量子失协的演化,同时给出了量子纠缠和量子失协的演化。研究结果表明:通过提高两原子间初始纠缠度及处于W态时的纯度可以提高系统的量子关联。耦合常数和光子数在量子关联演化过程中扮演了重要角色。

消相干环境下X-态量子关联的几何测量

在文献[1]的基础上,将文献[1]中求解出消相干环境下Bell对角态的GMQD(geometric measure of quantumdiscord)方法推广到求解具有普遍形式的X-态的GMQD,并在求出一般形式X-态在3种不同消干环境的GMQD后,将结果应用于Bell对角态进行验证,能得到与文献[1]一致的形式.

耦合量子比特在最大纠缠混合态下几何量子失协鲁棒性的研究

几何测量量子失协是量子关联的一种表达形式。结合利用量子纠缠和几何量子失协,运用解析和数值模拟的方法,对非马尔科夫过程中耦合量子比特系统的量子关联动力学特性进行了比较研究。研究结果表明,在一定的初始态下,由于环境耗散作用的存在,量子纠缠和几何量子失协都随时间做递减的动力学演化,但几何量子失协比量子纠缠的递减要慢一些。表明几何量子失协的生存时间长于量子纠缠,更能抵抗环境的耗散作用、鲁棒性更好。因此,量子关联也是实现量子信息处理的有用资源。

具有三体相互作用海森堡自旋链模型的纠缠与几何失协

近年来有研究发现量子失协可以度量非纠缠的量子关联,而且非纠缠的量子关联在量子通信和量子计算中起到很重要的作用.本文研究了磁场,两种三体相互作用,各向异性参数,耦合常数,温度等参数对同时具有两种三体相互作用海森堡XXZ自旋链系统的量子纠缠,几何失协的影响以及与量子相变的关系.研究表明:量子纠缠和几何失协都可以清晰的表征本模型系统的量子相变现象;随着XZX+YZY型三体相互作用的增加量子纠缠和几何失协即使在高温时也可达到最大值;几何失协比量子纠缠更全面地描述了量子关联;XZY-YZX型三体相互作用的增加对量子纠缠有抑制作用;XZY-YZX型三体相互作用在一定区域内的增加对几何失协有抑制作用,在另一区域的增加可使几何失协增大到一个稳定的非零值.增大磁场和自旋耦合常数,减小各向异性参数会使纠缠的临界温度变大;调节自旋耦合常数可更有效的使量子纠缠和几何失协在高温时仍有一个较大的值.同时发现,在磁场0<B<5和各向异性参数-1<J_Z<10的区域两种量子关联都可以维持在最大值.