Realization and characterization of a two-photon four-qubit linear cluster state

We report on the experimental realization of a four-qubit linear cluster state via two photons entangled both in polarization and linear momentum. This state was investigated by performing tomographic measurements and by evaluating an entanglement witness. By use of this state we carried out a novel nonlocality proof, the so-called "stronger two observer all-versus-nothing" test of quantum nonlocality.     

Testing the nonlocality of entangled states by a new Bell-like inequality

We test a new four-qubit entangled state by the former Bell-like inequalities and find that it violates these inequalities, but not maximally. According to this entangled state, we build a new Bell-like inequality, which is violated by this new state maximally. We also determine the nonlocality of some other four-qubit states by the new inequality. It is found that the new inequality acts as a strong entanglement witness for the new state. This can be used to test new entangled states experimentally.     

Einstein-Podolsky-Rosen Steering for Mixed Entangled Coherent States

By using the Born Markovian master equation, we study the relationship among the Einstein–Podolsky–Rosen (EPR) steering, Bell nonlocality, and quantum entanglement of entangled coherent states (ECSs) under decoherence. We illustrate the dynamical behavior of the three types of correlations for various optical field strength regimes. In general, we find that correlation measurements begin at their maximum and decline over time. We find that quantum steering and nonlocality behave similarly in terms of photon number during dynamics. Furthermore, we discover that ECSs with steerability can violate the Bell inequality, and that not every ECS with Bell nonlocality is steerable. In the current work, without the memory stored in the environment, some of the initial states with maximal values of quantum steering, Bell nonlocality, and entanglement can provide a delayed loss of that value during temporal evolution, which is of interest to the current study.     

The Essence of More Nonlocality with Less Entanglement in Bell Tests

In this paper, we will explore the essence of the phenomenon that state with less entanglement may generate greater Bell violation in the two-qubit Bell tests with CH-type inequalities, i.e., more nonlocality with less entanglement. We will show that this interesting but counterintuitive phenomenon is caused by the rotational asymmetry of the nonmaximally entangled state in the measurement plane. This asymmetry allows the both-side detection probabilities and the one-side detection probabilities obtain their maximal values with nonmaximally entangled state. But the maximal Bell violation may not always happen on nonmaximally entangled state, because these probabilities will compete with each other, and the Bell violation behaves differently for various CH-type inequalities.     

Minimizing the loss of entanglement under dimensional reduction

We investigate the possibility of transforming, under local operations and classical communication, a general bipartite quantum state on a d_A x d_B tensor-product space into a final state in 2 x 2 dimensions, while maintaining as much entanglement as possible. For pure states, we prove that Nielsens theorem provides the optimal protocol, and we present quantitative results on the degree of entanglement before and after the dimensional reduction. For mixed states, we identify a protocol that we argue is optimal for isotropic and Werner states. In the literature, it has been conjectured that some Werner states are bound entangled and in support of this conjecture our protocol gives final states without entanglement for this class of states. For all other entangled Werner states and for all entangled isotropic states some degree of free entanglement is maintained. In this sense, our protocol may be used to discriminate between bound and free entanglement.Received: 21 January 2004, Published online: 2 March 2004PACS: 03.67.Mn Entanglement production, characterization, and manipulation - 42.50.Dv Nonclassical states of the electromagnetic field, including entangled photon states; quantum state engineering and measurements - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.)     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Symmetric extensions of quantum States and local hidden variable theories

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and nonlocality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasiextension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.     

Quantum Entanglement in Concept Combinations

Research in the application of quantum structures to cognitive science confirms that these structures quite systematically appear in the dynamics of concepts and their combinations and quantum-based models faithfully represent experimental data of situations where classical approaches are problematical. In this paper, we analyze the data we collected in an experiment on a specific conceptual combination, showing that Bell’s inequalities are violated in the experiment. We present a new refined entanglement scheme to model these data within standard quantum theory rules, where ‘entangled measurements and entangled evolutions’ occur, in addition to the expected ‘entangled states’, and present a full quantum representation in complex Hilbert space of the data. This stronger form of entanglement in measurements and evolutions might have relevant applications in the foundations of quantum theory, as well as in the interpretation of nonlocality tests. It could indeed explain some non-negligible ‘anomalies’ identified in EPR-Bell experiments.     

纠缠薛定谔猫态的非局域性及其在热库中的演化

利用Bell-CHSH(Clauser-Horne-Shimony-Holt）不等式研究了两种纠缠的光学薛定猫态的量子非定域性及其在真空热库中的演化。计算表明，最大纠缠的薛定谔猫态具有最大非定域性。在真空热库中随着时间的演化，两种纠缠态的量子非定域性逐渐减弱直至消失。     

Quantum Measurement of Two-Qubit System in Damping Noise Environment

It is known that the inevitable interaction of the entangled qubits with their environments may result in the degradation of quantum correlation.We study the decoherence of two remote qubits under general local single-and two-sided amplitude-damping channel(ADC).By using concurrence,quantum discord and Clauser-Horne-ShimonyHolt(CHSH)inequality,we find that the relation between the residual quantum correlations and the initial ones are different.Recently,Wang et al.[Int.J.Theor.Phys.54(2015)5]showed that there exist a set of partially entangled states that are more robust than maximally entangled states in terms of the residual quantum correlation measured by concurrence,fully entangled fraction and quantum discord,respectively.Here we find that both in single-and two-sided ADC,only the evolution of CHSH inequality with the initial parameter is proportional to that of the initial nonlocality.That means the initial state with maximally nonlocality will retain its role in the evolution.It implies that the evolution of nonlocality may reveal the characteristics of quantum state better.Furthermore,we discuss the evolutions of the three different quantum measurements with the initial parameter under generalized amplitude damping channel(GADC)and find that they are all proportional to that of the initial state.     

远距离量子通信实验中的高维纠缠源

设计了适用于远距离量子通信实验的高维纠缠源.利用连续激光器抽运产生了极化-时间两体四维纠缠光子对,在抽运功率20 mW下测到每秒700对符合,保真度为89%±3%.相比已有的高维纠缠源,在本文中发展的源具有传输便利、相位稳定性好等优点,适用于未来远距离高维量子通信实验和量子力学基本问题实验检验,如远距离高维量子密码实验、两粒子Greenberger-Horne-Zeilinger定理检验、两粒子量子赝"心灵感应"(quantum pseudo telepathy)实验演示等. 关键词： 高维纠缠 极化纠缠 时间箱纠缠 量子通信     

Dynamical nonlocality of the entangled coherent state in the phase damping model

This paper studies the dynamics of nonlocality for a bosonic entangled coherent state in a phase damping model. The density operator of the system is solved by using a superoperator method. The dynamics of nonlocality for the bosonic entangled coherent state is uncovered by the Bell operator based on the pseudospin operator of a light field. The dynamics of the nonlocality for this state has also been studied by other Bell operators. The result of the numerical calculations of the Bell function shows that the quantum nonlocality heavily depends on the chosen Bell operator.     

Generalized Steering Robustness of Bipartite Quantum States

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR.     

Quantum correlations from local amplitudes and the resolution of the Einstein-Podolsky-Rosen nonlocality puzzle

The Einstein-Podolsky-Rosen (EPR) nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is more or less entirely resolved, if the quantum correlations are calculated directly from local quantities, which preserve the phase information in the quantum system. We assume strict locality for the probability amplitudes instead of local realism for the outcomes and calculate an amplitude correlation function. Then the experimentally observed correlation of outcomes is calculated from the square of the amplitude correlation function. Locality of amplitudes implies that measurement on one particle does not collapse the companion particle to a definite state. Apart from resolving the EPR puzzle, this approach shows that the physical interpretation of apparently “nonlocal” effects, such as quantum teleportation and entanglement swapping, are different from what is usually assumed. Bell-type measurements do not change distant states. Yet the correlations are correctly reproduced, when measured, if complex probability amplitudes are treated as the basic local quantities. As examples, we derive the quantum correlations of two-particle maximally entangled states and the three-particle Greenberger-Horne-Zeilinger entangled state.     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Single-Mode Excited GHZ-type Entangled Coherent State

A class of the single-mode excited GHZ-type entangled coherent states (EGHZECSs) are presented. we exhibit the remarkable properties of the single-mode EGHZECSs, depended on the excitation photon number, such as entanglement and nonlocality via investigating their concurrence of entanglement and examining their violation of CHSH inequality. Finally, we propose how to generate the EGHZECSs by using cavity QED and quantum measurement and by using BBO crystal and single-photon detection technique, respectively.     

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.     

纠缠相干态的纠缠浓缩

利用线性光学元器件对光场量子态进行操纵,可以实现远程的量子纠缠调控和量子通讯.通过分析光学分束器对相干态光场的作用,发现当初始光场态是两个两部分纠缠态的直乘时,让其中的两模通过光学分束器作用后再对其进行光子计数,另外两模将会塌缩到新的纠缠态.基于这个特点,提出了一个实现部分纠缠相干态纠缠浓缩的方案.在这个方案中,两个部分纠缠相干态被用来作为量子信道,通过光学分束器作用后对光场进行光子数探测时,如果测量到光场的两模分别处于奇光子数态和零光子数态,则光场另外的两模将塌缩到最大纠缠态,从而完成纠缠浓缩的过程.计算结果表明,对于纠缠相干态,无论其初始的纠缠是多么微弱,利用这种方法总有一定的几率可以从中提纯出最大纠缠态.     

The fully entangled fraction as an inclusive measure of entanglement applications

Characterizing entanglement in all but the simplest case of a two qubit pure state is a hard problem, even understanding the relevant experimental quantities that are related to entanglement is difficult. It may not be necessary, however, to quantify the entanglement of a state in order to quantify the quantum information processing significance of a state. It is known that the fully entangled fraction has a direct relationship to the fidelity of teleportation maximized under the actions of local unitary operations. In the case of two qubits we point out that the fully entangled fraction can also be related to the fidelities, maximized under the actions of local unitary operations, of other important quantum information tasks such as dense coding, entanglement swapping and quantum cryptography in such a way as to provide an inclusive measure of these entanglement applications. For two qubit systems the fully entangled fraction has a simple known closed-form expression and we establish lower and upper bounds of this quantity with the concurrence. This approach is readily extendable to more complicated systems.