Measurement of ‘closeness’ and Distinguishability of the Quantum States in Yang-Baxter Systems

Under the actions of different Hamiltonians on the different two-qubit input states by using the quantum Yang-Baxterization approach, we investigate the behaviors of the fidelity and the trace distance as measures of ‘closeness’ and distinguishability of two quantum states. The results show that the fidelity that is the main figure of merit for any communication and computing process can be kept to high values depending on the choice of the initial states and the Hamiltonians constructed by the Yang-Baxter equation. On the other hand, by choosing the initial states and Yang-Baxter systems which are the various extensions of the Yang-Baxter equations for several matrices, these quantifiers can be adjusted as desired to achieve many quantum computing and computational tasks. Furthermore, to quantify the performance of quantum teleportation we examine the teleportation fidelity for the outputs that correspond to the different two-qubit X-type states under the actions of the different Hamiltonians. It is possible to obtain high fidelity to use the quantum teleportation process.

     

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.     

Quantum Discord in Two-Qubit System Constructed from the Yang–Baxter Equation

Quantum correlations among parts of a composite quantum system are a fundamental resource for several applications in quantum information. In general, quantum discord can measure quantum correlations. In that way, we investigate the quantum discord of the two-qubit system constructed from the Yang-Baxter Equation. The density matrix of this system is generated through the unitary Yang-Baxter matrix R. The analytical expression and numerical result of quantum discord and geometric measure of quantum discord are obtained for the Yang-Baxter system. These results show that quantum discord and geometric measure of quantum discord are only connect with the parameter θ, which is the important spectral parameter in Yang Baxter equation.     

Deterministic joint remote preparation of an arbitrary two-qubit state in the presence of noise

Using two tripartite Greenberger-Horne-Zeilinger （GHZ） states as the shared channels, we investigate the noise effects on the deterministic joint remote preparation of an arbitrary two-qubit state. By unitary matrix decomposition procedure, we first construct the quantum logic circuit of the deterministic joint remote state preparation protocol. Then, we analytically derive the fidelity and the average fidelity for the deterministic joint remote preparation of an arbitrary two- qubit state and of four types of special two-qubit states under the influence of the Pauli noises. It is found that the fidelity depends on the noise types, the qubit-environment coupling strength, and the state to be remotely prepared. Moreover, even if the two GHZ channels are subject to the same environmental noises, the average fidelities for remotely preparing different two-qubit states display different time evolution behaviors. The remote preparation of the identical two-qubit states also shows that the average fidelities affected by different noisy environments exhibit different evolution actions.     

Robustness of quantum correlations against decoherence

We study dynamics of nonclassical correlations by exactly solving a model consisting of two atomic qubits with spontaneous emission. We find that the nonclassical correlations defined by different measures give different qualitative characterizations of those correlations. The relative behaviors of those correlation measures are presented explicitly for various quantum states in the two-qubit atomic system. In particular, we find that the robustness of quantum correlations can be greatly enhanced by performing appropriate local unitary operations on the initial state of the system.     

Detecting Quantum Dissonance and Discord in Exact Dynamics of qubit Systems

In this paper, we evaluate the quantum and classical correlations in exact dynamics of qubit systems interacting with a common dephasing environment. We show the existence of a sharp transition between the classical and quantum loss of correlations during the time evolution. We show that it is possible to exploit a large class of initial states in different tasks of quantum information and processing without any perturbation of the correlations from the environment noisy for large time intervals. On the other hand, we include the dynamics of a new kind of correlation so-called quantum dissonance, which contains the rest of the nonclassical correlations. We show that the quantum dissonance can be considered as an indicator to expect the behavior of the dynamics of classical and quantum correlations in composite open quantum systems.     

杨-巴克斯特自旋1/2链模型的量子关联研究

量子系统各部分间的量子关联可以作为量子信息应用研究的基础资源. 而量子失协是度量量子关联大小的物理量. 由此研究杨-巴克斯特自旋1/2链模型的量子关联情况. 首先利用两个杨-巴克斯特方程的解得到相应的杨-巴克斯特自旋1/2链模型. 然后, 计算分析热平衡时杨-巴克斯特自旋1/2链模型的量子失协、几何量子失协和量子纠缠随着温度和外磁场的变化情况. 结果表明对于杨-巴克斯特自旋1/2链模型, 量子失协和几何量子失协能够比量子纠缠更好地度量量子关联.     

Quantum entanglement and quantum operation

It is a simple introduction to quantum entanglement and quantum operations. The authors focus on some applications of quantum entanglement and relations between two-qubit entangled states and unitary operations. It includes remote state preparation by using any pure entangled states, nonlocal operation implementation using entangled states, entanglement capacity of two-qubit gates and two-qubit gates construction. Supported by the National Fundamental Research Program of China (Grant No. 2001CB309306), the National Natural Science Foundation of China (Grant Nos. 60621064 and 10674127) and the Innovation Funds from Chinese Academy of Sciences     

两量子比特非线性相互作用模型中的量子关联

运用量子态变换的方法论证了两个qubit纯态中量子关联与纠缠的等价性.并利用三种带有横场的非线性相互作用模型研究了两个qubit体系中的量子关联.发现合适的横场对于最大量子关联态的获得、平均量子关联的提高都有着积极的作用.两个qubit体系获得最大量子关联时,不同模型,不同的横场,对应的量子态却各不相同.     

Controlling transfer of quantum correlations among bi-partitions of a composite quantum system by combining different noisy environments

The correlation dynamics are investigated for various bi-partitions of a composite quantum system consisting of two qubits and two independent and non-identical noisy environments. The two qubits have no direct interaction with each other and locally interact with their environments. Classical and quantum correlations including the entanglement are initially prepared only between the two qubits. We find that contrary to the identical noisy environment case, the quantum correlation transfer direction can be controlled by combining different noisy environments. The amplitude-damping environment determines whether there exists the entanglement transfer among bi-partitions of the system. When one qubit is coupled to an amplitude-damping environment and the other one to a bit-flip one, we find a very interesting result that all the quantum and the classical correlations, and even the entanglement, originally existing between the qubits, can be completely transferred without any loss to the qubit coupled to the bit-flit environment and the amplitude-damping environment. We also notice that it is possible to distinguish the quantum correlation from the classical correlation and the entanglement by combining different noisy environments.     

Decoherence from a spin chain with Dzyaloshinskii—Moriya interaction

We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya interaction.In the case of a two-qubit with an initial pure state,quantum correlations decay to zero at the critical point of the environment in a very short time.In the case of a two-qubit with initial mixed state,it is found that quantum discord may get maximized due to the quantum critical behavior of the environment,while entanglement vanishes under the same condition.Besides,we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment.The effects of Dzyaloshinsky-Moriya interaction on quantum correlations are considered in the two cases.The decay of quantum correlations is always strengthened by Dzyaloshinsky-Moriya interaction.     

Braid Group Representation and Solutions of the Quantum Yang-Baxter Equation Associated with 10-Dimensional Representation of SU(4)

The braid group representation associated with the 10-dimensional representation of SU(4) is derived, based on the weight conservation and extended Kauffman diagrammatic technique. The corresponding trigonometric and rational solutions of the quantum Yang-Baxter equations are constructed in terms of the Yang-Baxterization procedure.     

Controlled-phase operation on two remote charge qubits via conditional electron dynamics in auxiliary structure

We study a possibility of implementation of two-qubit operations in an array of semiconductor quantum-dot-based charge qubits without the use of direct interqubit coupling. For that purpose, we exploit a sequence of laser-induced single-electron transfers in an auxiliary quantum dot structure whose transport properties depend on qubit states. As is demonstrated, it brings about the accumulation of additional phases that are specific for each of two-qubit logical states. Those phases depend on the laser and structure parameters. As the result, choosing them appropriately, one can obtain the desired two-qubit phase evolution.     

Controlled phase gates based on two nonidentical quantum dots trapped in separate cavities

We propose a scheme for realizing two-qubit controlled phase gates on two nonidentical quantum dots trapped in separate cavities. In our scheme, each dot simultaneously interacts with one highly detuned cavity mode and two strong driven classical fields. During the gate operation, the quantum dots undergo no transition, while the system can acquire different phases conditional on different states of the quantum dots. With the application of the single-qubit operations, two-qubit controlled phase gates can be realized.     

Robustness of Entanglement During Decoherence

Finding the most robust entangled states during the whole process of decoherence is a particularly fundamental problem for quantum physics and quantum information processing. In this paper, the decoherence process of two-qubit system under two individual identical decoherence channels is investigated systematically. We find that although the robustness of two-qubit states with same initial entanglement is usually different, the Bell-like states are always the most robust entangled states during decoherence. That is to say, affected by the same amount of noise, the remain entanglement of an arbitrary two-qubit state is not more than that of a Bell-like state with the same initial entanglement.     

Effects of Noise on Joint Remote State Preparation of an Arbitrary Equatorial Two-Qubit State

By using a six-qubit cluster state as the quantum channel, we investigat the joint remote state preparation of an arbitrary equatorial two-qubit state. We analytically obtain the fidelities of the joint remote state preparation process in noisy environments, such as the amplitude-damping noise and phase-damping noise. In our scheme, the two different noise including amplitude-damping noise and the phase-damping noise only affect the travel qubits of the quantum channel, and then we show that the fidelities in these two noisy cases only depend on the decoherence noisy rate.     

Direct measurement of two-qubit phononic entangled states via optomechanical interactions

We propose schemes of direct concurrence measurement for two-qubit phononic states from quantized mechanical vibration. By combining the Mach-Zehnder interferometer with the optomechanical cross-Kerr nonlinear effect, direct concurrence measurement schemes for two-qubit phononic entangled states are achieved with the help of photon detection with respect to the output of the interferometer. For different types of entangled states, diversified quantum devices and operations are designed accordingly. The final analysis shows reasonable performance under the current parameter conditions. Our schemes may be useful for potential phonon-based quantum computation and information in the future.     

Observable measure of bipartite quantum correlations

We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.     

Optimal subsystem approach to multi-qubit quantum state discrimination and experimental investigation

Quantum computing is a significant computing capability which is superior to classical computing because of its superposition feature. Distinguishing several quantum states from quantum algorithm outputs is often a vital computational task. In most cases, the quantum states tend to be non-orthogonal due to superposition; quantum mechanics has proved that perfect outcomes could not be achieved by measurements, forcing repetitive measurement. Hence, it is important to determine the optimum measuring method which requires fewer repetitions and a lower error rate. However, extending current measurement approaches mainly aiming at quantum cryptography to multi-qubit situations for quantum computing confronts challenges, such as conducting global operations which has considerable costs in the experimental realm. Therefore, in this study, we have proposed an optimum subsystem method to avoid these difficulties. We have provided an analysis of the comparison between the reduced subsystem method and the global minimum error method for two-qubit problems; the conclusions have been verified experimentally. The results showed that the subsystem method could effectively discriminate non-orthogonal two-qubit states, such as separable states, entangled pure states, and mixed states; the cost of the experimental process had been significantly reduced, in most circumstances, with acceptable error rate. We believe the optimal subsystem method is the most valuable and promising approach for multi-qubit quantum computing applications.     

飞秒激光直写光量子逻辑门

量子比特在同一时刻可处于所有可能状态上的叠加特性使得量子计算机具有天然的并行计算能力,在处理某些特定问题时具有超越经典计算机的明显优势.飞秒激光直写技术因其具有单步骤高效加工真三维光波导回路的能力,在制备通用型集成光量子计算机的基本单元—量子逻辑门中发挥着越来越重要的作用.本文综述了飞秒激光直写由定向耦合器构成的光量子比特逻辑门的进展.主要包括定向耦合器的功能、构成、直写和性能表征,集成波片、哈达玛门和泡利交换门等单量子比特逻辑门、受控非门和受控相位门等两量子比特逻辑门的直写加工,并对飞秒激光加工三量子比特逻辑门进行了展望.