Quantum Cluster Algebra Structure on the Quantum Grothendieck Ring K_(t-1)

In this paper, we give a quantum cluster algebra structure on the deformed Grothendieck ring Kt-1 which is defined in section 2.

Recursive formulas for the Kronecker quantum cluster algebra with principal coefficients

We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients.As a byproduct,we obtain two barinvariant positive ZP-bases with one being the atomic basis.

Bases of the Quantum Cluster Algebra of the Kronecker Quiver

We construct bar-invariant Z[q ±1/2]-bases of the quantum cluster algebra of Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the corresponding cluster algebra. As a byproduct, we prove positivity of the elements in these bases.

An efficient deterministic secure quantum communication scheme based on cluster states and identity authentication

A novel efficient deterministic secure quantum communication scheme based on four-qubit cluster states and single-photon identity authentication is proposed. In this scheme, the two authenticated users can transmit two bits of classical information per cluster state, and its efficiency of the quantum communication is 1/3, which is approximately 1.67 times that of the previous protocol presented by Wang et al [Chin. Phys. Lett. 23 （2006） 2658]. Security analysis shows the present scheme is secure against intercept-resend attack and the impersonator＇s attack. Furthermore, it is more economic with present-day techniques and easily processed by a one-way quantum computer.

Hierarchical and probabilistic quantum information splitting of an arbitrary two-qubit state via two cluster states

Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements,and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement（POVM） instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.

Cluster algebra structure on the finite dimensional representations of affine quantum group U_q(_3)

In this paper, we prove one case of conjecture given by Hemandez and Leclerc. We give a cluster algebra structuure on the Grothendieck ring of a full subcategory of the finite dimensional representations of affine quantum group Uq（A3）. As a conclusion, for every exchange relation of cluster algebra, there exists an exact sequence of the full subcategory corresponding to it.

Violation of Cluster Property in Quantum Antiferromagnet

The cluster property is one of fundamental properties in physics. This property means that there are no relations between two events that are sufficiently separated. Because the cluster property is directly connected with entanglement in quantum field theory and in many-body systems, theoretical and experimental progress on entanglement stimulates us to study this property deeply. In this paper we investigate the cluster property in the spin 1/2 XXZ antiferromagnet on the square lattice with an explicitly symmetry breaking interaction of strength g. In this model spontaneous symmetry breaking occurs when the lattice size N is infinitely large. On the other hand, we have to make g zero in order to obtain quantities in the XXZ model with no symmetry breaking interaction. Since some results depend on the sequence of limit operations — ?and , it is difficult to draw a clear conclusion in these limits. Therefore we study the model with finite g on the finite lattice, whose size N is supposed to be 1020, for our quantitative calculations. Then we can obtain the concrete ground state. In order to study the cluster property we calculate the spin correlation function. It is known that the function due to Nambu-Goldstone mode (gapless mode), which is calculated using linear spin wave theory, satisfies this property. In this paper we show that almost degenerate states also induce the spin correlation. We assume that the spin correlation function in measurements is a sum of the function due to Nambu-Goldstone mode and one due to these degenerate states. Then we examine whether the additional correlation function violates the cluster property or not. Our conclusion is that this function is finite at any distance, which means the violation of the cluster property, and it is of order of . Except for the case of extremely small g, this violation is the fine effect. Therefore the correlation function due to the degenerate states can be observed only when it is larger than the spin correlation function due to Nambu-Goldstone mode. We show that g required for this condition depends on the distance between positions of two spin operators.

Quantum Curie-Weiss Magnet Induced by Violation of Cluster Property

There are some concepts that are accepted in our daily life but are not trivial in physics. One of them is the cluster property that means there exist no relations between two events which are sufficiently separated. In the works recently published by the author, the extensive and quantitative examination has been made about the violation of cluster property in the correlation function of the spin operator for the quantum spin system. These works have shown that, when we include the symmetry breaking interaction, the effect by the violation is proportional to the inverse of the system size. Therefore this effect is tinny since the system size is quite large. In order to find the effect due to the violation even when the size is large, we propose a new system where additional spins couple with the spin system on the square lattice, where the coupling constant between these systems being assumed to be small. Applying the perturbation theory, we obtain the effective Hamiltonian for the additional system. This Hamiltonian includes Curie-Weiss model that is induced by the violation of the cluster property. Then we find that this effective Hamiltonian has the factor which is the inverse of the system size. Since Curie-Weiss model, which is known to be exactly soluble, has to contain this factor so that the thermodynamical properties are well-defined, the essential factor for the Hamiltonian is determined by the coupling and the strength of the symmetry breaking interaction. Our conclusion is, therefore, that it is possible to observe the effect by the violation of the cluster property at the inverse temperature whose order is given by these parameters.

A Quantum Chemical Study on Hexanuclear Cluster Halides of Rare Earth Elements and Their Interstitial Compounds

The electronic structures of rare earth cluster halides R(R_6X_(12)) and their interstitial compounds R_7X_(12)Z were studied by the DV-X_(?) method (R=Sc,Y,Pr,Gd or Er;X=Cl,Br or I;Z=B,C,N,Fe,Co or Ru).The results show that because f electrons in empty rare earth cluster are screened,their orbitals are more difficult to overlap each other,a deficiency of skeleton orbitals in cluster causing the system to be unstable.They are easily condensed into chain compound R_2X_3 or R_5X_8.If a light atom of main group is embedded into octahedral cluster,bonding orbitals formed from interstitial atom and rare earth cluster strengthen cluster skeleton bond in the system to reach structural stability.If embedded atom belongs to transition metal,bonding orbitals composed of that of interstitial atom and rare earth cluster take the place of original cluster skeleton orbitals to form heteronuclear metal cluster (or double-coordination compound).

Controlled quantum state sharing of arbitrary two-qubit states with five-qubit cluster states

In this paper, we propose a controlled quantum state sharing scheme to share an arbitrary two-qubit state using a five-qubit cluster state and the Bell state measurement. In this scheme, the five-qubit cluster state is shared by a sender （Alice）, a controller （Charlie）, and a receiver （Bob）, and the sender only needs to perform the Bell-state measurements on her particles during the quantum state sharing process, the controller performs a single-qubit projective measurement on his particles, then the receiver can reconstruct the arbitrary two-qubit state by performing some appropriate unitary transformations on his particles after he has known the measured results of the sender and the controller.

Clustering Algorithm of Quantum Self-Organization Network

To enhance the clustering ability of self-organization network, this paper introduces a quantum inspired self-organization clustering algorithm. First, the clustering samples and the weight values in the competitive layer are mapped to the qubits on the Bloch sphere, and then, the winning node is obtained by computing the spherical distance between sample and weight value. Finally, the weight values of the winning nodes and its neighborhood are updated by rotating them to the sample on the Bloch sphere until the convergence. The clustering results of IRIS sample show that the proposed approach is obviously superior to the classical self-organization network and the K-mean clustering algorithm.

The Cluster Fe₂Si₁₈as the New Quantum Bit System

Multiconfiguration quantum chemical calculation of geometry and electron properties of Fe2Si18 cluster indicates on the predictable change of spin states as a function of the excitation energy beginning from ground state with the total spin S = 4. The charges on the two Fe atoms are quite different as well as the charge distribution on the surrounding Si atoms. Nevertheless the total dipole moment of the cluster is a monotonically decreasing function of the excitation energy and it reaches practically zero value in the first singlet state in which the cluster represents a new version of a quibit system.

基于cluster态任意单粒子态可控量子信息共享

基于cluster态具有较强的纠缠顽固性,提出两个利用四粒子cluster态传送任意单粒子态的量子信息共享方案.第一个方案中发送者Alice、控制者Charlie和接收者Bob共享一个四粒子纠缠态,首先Alice对自己拥有的粒子执行一个三粒子Von-Neumann联合测量,然后Charlie对其拥有粒子执行Z基测量,最后Bob根据发送者和控制者的测量结果,对所拥有的粒子做适当的幺正变换,就能重建共享的单粒子任意态.第二个方案利用一个辅助粒子,发送者Alice、控制者Charlie只需做Bell基测量,Bob通过比特位翻转和幺正变换即可得到Alice传送的量子态.与已有方案相比,两方案信息共享的成功概率为100%,且只需四粒子cluster态为载体,可在目前实验室技术条件下实现.

基于Cluster态的量子通信(英文)

提出基于Cluster态量子对话,这使得合法双方可以直接交换4位秘密信息。和3粒子W态相比较,此协议有以下优点:经过两步安全检查后,通过单光子发射和两位经典信息的帮助,可以相互传输4比特秘密信息。还可以克服拦截重发攻击、纠缠测量攻击和最优化非相干攻击。

腔QED中cluster相干态的产生(英文)

提出一个在腔QED中产生cluster-型纠缠相干态的方案。基于三能级A型原子和双模腔场之间的大失谐相互作用,原子的自发辐射可以忽略。此外,腔场的初态是真空态。在这个方案中,对原子进行测量后,能够产生腔场cluster-型纠缠相干态,并讨论了实验的可行性。

利用cluster态实现任意两粒子纠缠态的概率隐形传态(英文)

提出两个概率隐形传态方案,这两个方案都是以一个四粒子cluster非最大纠缠态作为量子信道来实现未知两粒子纠缠态的隐形传态。在第一个方案中传送的是一个特殊的两粒子纠缠态,此纠缠态可以实现一定的概率传输,此概率由cluster态中绝对值较小的两个系数决定。在第二个方案中,传送的是任意两粒子纠缠态,与第一方案相比,Bob除了需要实施幺正变换外,还要实施量子控制相位门才能重建被传送的纠缠态。使用非最大纠缠cluster态作为量子信道可以节约更多的纠缠资源和经典信息。

通过cluster态实现两粒子纠缠态的量子几率隐形传态(英文)

提出通过一个四粒子cluster非最大纠缠态作为量子信道来实现一未知两粒子纠缠态的量子几率隐形传态方案。在此方案中,纠缠态可以实现一定的几率传输,此几率由cluster态中绝对值较小的两个系数决定。如果我们用cluster最大纠缠态作为量子信道,此时几率隐形传态就成了一般的隐形传态,即成功传输的几率为100%。

基于四粒子cluster态的N位量子态秘密共享方案

为了实现N位量子态秘密共享,提出利用四粒子cluster态作为量子信道,cluster态虽然不是最大的纠缠态,但是有比最大纠缠态更强健的性质,通信者Alice通过添加辅助粒子,并对量子态进行五粒子联合测量,Bob(Charlie)对手中的粒子进行单粒子测量,并把结果和恢复量子态需要进行的操作告知Charlie(Bob),Charlie(Bob)按照从Bob(Charlie)处得到的信息对手中的粒子进行相应的操作,最后再根据需要,把量子态通过相应的量子线路得到所需要共享的量子态。安全性分析证明此方案是安全的。

Cluster态的量子签名方案

提出一种利用Clusterstate纠缠态实现的量子签名方案。该方案中用Cluster态作为量子信道,每一组量子比特串分别分发给消息拥有和签名者Alice、公证人TA、验签名者Bob。加载消息的方法是Alice在TA规定量子比特串序列下,分别对拥有的量子比特对的第一个量子比特进行幺正变换操作而进行。对拥有的量子比特对进行的Bell测量结果是消息的签名。Bob对拥有的对应的两个量子比特对进行Bell测量来验证签名,但要得到公证人TA对其约束才能完成。Cluster state纠缠态在纠缠特性、局域操作保真性和安全性有较好的性能。

利用四原子Cluster态概率隐形传送两原子纠缠态

提出两个二能级原子纠缠态的隐形传态方案,方案中选用由四个全同二能级原子组成的非最大纠缠Cluster态作为量子信道.研究表明,接收者根据发送者传送的经典信息,通过引入一个附加原子并实施相应的幺正变化,即可以一定的概率重构原子态,此概率由Cluster态中绝对值最小的两个系数决定.该方案中使用的是Cluster非最大纠缠态作为量子信道,因此与其他方案相比该方案可以节约更多的纠缠资源和经典信息.如果使用Cluster最大纠缠态作为量子信道,那么此方案即为一般的量子传态方案,成功传送的概率为100%.