Scaling of entanglement close to a quantum phase transition

Classical phase transitions occur when a physical system reaches a state below a critical temperature characterized by macroscopic order. Quantum phase transitions occur at absolute zero; they are induced by the change of an external parameter or coupling constant, and are driven by quantum fluctuations. Examples include transitions in quantum Hall systems, localization in Si-MOSFETs (metal oxide silicon field-effect transistors; ref. 4) and the superconductor-insulator transition in two-dimensional systems. Both classical and quantum critical points are governed by a diverging correlation length, although quantum systems possess additional correlations that do not have a classical counterpart. This phenomenon, known as entanglement, is the resource that enables quantum computation and communication. The role of entanglement at a phase transition is not captured by statistical mechanics-a complete classification of the critical many-body state requires the introduction of concepts from quantum information theory. Here we connect the theory of critical phenomena with quantum information by exploring the entangling resources of a system close to its quantum critical point. We demonstrate, for a class of one-dimensional magnetic systems, that entanglement shows scaling behaviour in the vicinity of the transition point.     

Entanglement in a solid-state spin ensemble

Entanglement is the quintessential quantum phenomenon. It is a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing and the strongest forms of quantum cryptography. Spin ensembles, such as those used in liquid-state nuclear magnetic resonance, have been important for the development of quantum control methods. However, these demonstrations contain no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclear spins in isotopically engineered, phosphorus-doped silicon. We combined high-field (3.4?T), low-temperature (2.9?K) electron spin resonance with hyperpolarization of the (31)P nuclear spin to obtain an initial state of sufficient purity to create a non-classical, inseparable state. The state was verified using density matrix tomography based on geometric phase gates, and had a fidelity of 98% relative to the ideal state at this field and temperature. The entanglement operation was performed simultaneously, with high fidelity, on 10(10) spin pairs; this fulfils one of the essential requirements for a silicon-based quantum information processor.     

Preparation and measurement of three-qubit entanglement in a superconducting circuit

Traditionally, quantum entanglement has been central to foundational discussions of quantum mechanics. The measurement of correlations between entangled particles can have results at odds with classical behaviour. These discrepancies grow exponentially with the number of entangled particles. With the ample experimental confirmation of quantum mechanical predictions, entanglement has evolved from a philosophical conundrum into a key resource for technologies such as quantum communication and computation. Although entanglement in superconducting circuits has been limited so far to two qubits, the extension of entanglement to three, eight and ten qubits has been achieved among spins, ions and photons, respectively. A key question for solid-state quantum information processing is whether an engineered system could display the multi-qubit entanglement necessary for quantum error correction, which starts with tripartite entanglement. Here, using a circuit quantum electrodynamics architecture, we demonstrate deterministic production of three-qubit Greenberger-Horne-Zeilinger (GHZ) states with fidelity of 88 per cent, measured with quantum state tomography. Several entanglement witnesses detect genuine three-qubit entanglement by violating biseparable bounds by 830?±?80 per cent. We demonstrate the first step of basic quantum error correction, namely the encoding of a logical qubit into a manifold of GHZ-like states using a repetition code. The integration of this encoding with decoding and error-correcting steps in a feedback loop will be the next step for quantum computing with integrated circuits.     

两光子的自旋态与纠缠态

用量子理论方法给出两光子的自旋态, 即通过2个单光子自旋态的直积并叠加得到两光子的自旋本征态, 从而给出两光子的纠缠态, 所得结果与用经典极化矢量表示的两光子纠缠态不同, 该结果可应用于量子通讯和量子计算中.     

量子纠缠态

量子纠缠态是量子力学的精髓,纠缠态在量子计算和量子通讯中起着重要作用．本文系统的介绍了量子纠缠态,从他的起源、定义、常见纠缠态及纠缠度进行了说明。     

Generation of three-qubit entangled states using superconducting phase qubits

Entanglement is one of the key resources required for quantum computation, so the experimental creation and measurement of entangled states is of crucial importance for various physical implementations of quantum computers. In superconducting devices, two-qubit entangled states have been demonstrated and used to show violations of Bell's inequality and to implement simple quantum algorithms. Unlike the two-qubit case, where all maximally entangled two-qubit states are equivalent up to local changes of basis, three qubits can be entangled in two fundamentally different ways. These are typified by the states |GHZ>= (|000+?|111>)/ sqrt [2] and |W>= (|001>?+?|010>?+?|100>)/ sqrt [3]. Here we demonstrate the operation of three coupled superconducting phase qubits and use them to create and measure |GHZ> and |W>states. The states are fully characterized using quantum state tomography and are shown to satisfy entanglement witnesses, confirming that they are indeed examples of three-qubit entanglement and are not separable into mixtures of two-qubit entanglement.     

An error-free protocol for quantum entanglement distribution in long-distance quantum communication

Quantum entanglement distribution is an essential part of quantum communication and computation protocols. Here, linear optic elements are employed for the distribution of quantum entanglement over a long distance. Polarization beam splitters and wave plates are used to realize an error-free protocol for broadcasting quantum entanglement in optical quantum communication. This protocol can determine the maximum distance of quantum communication without decoherence. Error detection and error correc-tion are performed in the proposed scheme. In other words, if there is a bit flip along the quantum channel, the end stations (Alice and Bob) can detect this state change and obtain the correct state (entangled photon) at another port. Existing general error detec-tion protocols are based on the quantum controlled-NOT (CNOT) or similar quantum logic operations, which are very difficult to implement experimentally. Here we present a feasible scheme for the implementation of entanglement distribution based on a linear optics element that does not need a quantum CNOT gate.     

Experimental demonstration of five-photon entanglement and open-destination teleportation

Quantum-mechanical entanglement of three or four particles has been achieved experimentally, and has been used to demonstrate the extreme contradiction between quantum mechanics and local realism. However, the realization of five-particle entanglement remains an experimental challenge. The ability to manipulate the entanglement of five or more particles is required for universal quantum error correction. Another key process in distributed quantum information processing, similar to encoding and decoding, is a teleportation protocol that we term 'open-destination' teleportation. An unknown quantum state of a single particle is teleported onto a superposition of N particles; at a later stage, this teleported state can be read out (for further applications) at any of the N particles, by a projection measurement on the remaining particles. Here we report a proof-of-principle demonstration of five-photon entanglement and open-destination teleportation (for N = 3). In the experiment, we use two entangled photon pairs to generate a four-photon entangled state, which is then combined with a single-photon state. Our experimental methods can be used for investigations of measurement-based quantum computation and multi-party quantum communication.     

量子关联研究综述

由EPR佯谬,薛定谔“猫态”等超越直观的纯量子现象产生的量子纠缠理论从其概念提出以来一直被人们认为既是量子理论最为重要的概念之一,也是在量子通讯中实现“稠密编码”和“隐形传态”的关键。然而,最近研究结果显示,量子纠缠并不能够完全解释量子关联所有特性。人们发现,除了纠缠以外,还存在对量子信息和量子计算具有极其重要意义的其它非经典关联,如量子失协是一个纯量子比特确定性量子计算机具有计算效率的原因。这说明,量子失协完全可以成为量子计算新的一种资源。文章介绍了非经典关联（包括量子纠缠）的基本概念及其度量方法,对量子失协在各类模型中表现出的量子关联特性进行分析和与量子纠缠,经典关联比较,从而体现出在各类量子体系中对量子失协进行研究的意义,同时引导理论和实验研究者去研究量子失协的潜在研究价值。     

Quantum-enhanced positioning and clock synchronization

A wide variety of positioning and ranging procedures are based on repeatedly sending electromagnetic pulses through space and measuring their time of arrival. The accuracy of such procedures is classically limited by the available power and bandwidth. Quantum entanglement and squeezing have been exploited in the context of interferometry, frequency measurements, lithography and algorithms. Here we report that quantum entanglement and squeezing can also be employed to overcome the classical limits in procedures such as positioning systems, clock synchronization and ranging. Our use of frequency-entangled pulses to construct quantum versions of these protocols results in enhanced accuracy compared with their classical analogues. We describe in detail the problem of establishing a position with respect to a fixed array of reference points.     

量子信道对纠缠鲁棒性的影响

考虑量子信道对多体纠缠鲁棒性的影响. 先根据可分态之集为一个凸闭集, 证明可以取到纠缠鲁棒性定义中的下确界, 再证明同一纠缠态ρ的两个最优态的凸组合仍是最优态, 纠缠鲁棒性作为定义态集合上函数是下半连续的; 最后, 分别给出一个量子信道不增加、 不减少[KG*8]及保持所有量子态的纠缠鲁棒性的充分必
要条件.     

Measurement-induced entanglement for excitation stored in remote atomic ensembles

A critical requirement for diverse applications in quantum information science is the capability to disseminate quantum resources over complex quantum networks. For example, the coherent distribution of entangled quantum states together with quantum memory (for storing the states) can enable scalable architectures for quantum computation, communication and metrology. Here we report observations of entanglement between two atomic ensembles located in distinct, spatially separated set-ups. Quantum interference in the detection of a photon emitted by one of the samples projects the otherwise independent ensembles into an entangled state with one joint excitation stored remotely in 10(5) atoms at each site. After a programmable delay, we confirm entanglement by mapping the state of the atoms to optical fields and measuring mutual coherences and photon statistics for these fields. We thereby determine a quantitative lower bound for the entanglement of the joint state of the ensembles. Our observations represent significant progress in the ability to distribute and store entangled quantum states.     

Experimental extraction of an entangled photon pair from two identically decohered pairs

Entanglement is considered to be one of the most important resources in quantum information processing schemes, including teleportation, dense coding and entanglement-based quantum key distribution. Because entanglement cannot be generated by classical communication between distant parties, distribution of entangled particles between them is necessary. During the distribution process, entanglement between the particles is degraded by the decoherence and dissipation processes that result from unavoidable coupling with the environment. Entanglement distillation and concentration schemes are therefore needed to extract pairs with a higher degree of entanglement from these less-entangled pairs; this is accomplished using local operations and classical communication. Here we report an experimental demonstration of extraction of a polarization-entangled photon pair from two decohered photon pairs. Two polarization-entangled photon pairs are generated by spontaneous parametric down-conversion and then distributed through a channel that induces identical phase fluctuations to both pairs; this ensures that no entanglement is available as long as each pair is manipulated individually. Then, through collective local operations and classical communication we extract from the two decohered pairs a photon pair that is observed to be polarization-entangled.     

两全同二能级原子同时与真空腔场相互作用任意态的纠缠

应用负值量子条件熵,研究了在大失谐情况下,两全同二能级原子同时与一真空腔场相互作用任意态纠缠的时间演化.考察了统初态对两原子系之间量子纠缠的影响,并将结果与concurrence的时间演化作了比较.结果表明,负值条件熵能够作为该条件下两全同二能级原子同时与单模腔场相互作用任意态的,容易解析计算的纠缠度.图2,参12.     

量子算法及其在图像处理中的应用

量子计算与量子信息是涉及物理学、计算机科学、数学以及信息科学等多个学科的新兴综合性交叉研究领域,是量子力学理论和经典计算理论完美结合的产物.由于其强大的计算能力及广阔的应用前景,使得其在国际学术界以及政府科研机构中引起巨大的兴趣.在量子计算的研究中,计算性能的优越性主要体现在算法的有效性上.目前为止,被公认的最具代表性的量子算法有Shor的大数质因子分解算法以及Grover提出的数据库搜索量子算法.集合运算是科学技术很多领域的基础,如数据库操作、信号处理、图像压缩等等都可最终归结为对集合的操作.但是对于包含了高维无序向量的集合,要对其进行有效快速的集合运算,在经典电子计算机上是困难的.因此,需要新的原理和新的算法来有效操作集合.量子图像处理(QIP)就是利用量子计算机来处理图像信息从而希望获得比电子计算机更好的处理效果.量子图像处理研究才刚刚起步,在不久的将来可能会成为一个受关注的研究热点.对目前的量子算法研究进展、量子集合运算、量子图像处理以及量子Hopfield神经网络研究作一个综述性论述.     

两种情形下两原子的纠缠演化特性

通过negativity方法,研究了两个空间分离的纠缠二能级原子依次通过高Q粒子数场时,两个原子的纠缠演化特性,发现：初始原子状态和光场状态对两原子的纠缠有明显的影响．通过选择初始状态可以得到较长时间的最大纠缠．然后与两个纠缠原子同时在高Q粒子真空场时两原子纠缠的演化做了有意义的比较,结果表明：当反映原子初始状态的参数θ〈π/2时,两种情形的纠缠演化趋势大致相同．当θ〈π/2时,纠缠演化大不一样．     

一类正线性映射的可分解性和最优性

非完全正的正线性映射在判定复合系统量子态的纠缠性中起关键作用.文章研究一类非完全正的正线性映射的性质,证明了此类正线性映射φ是可分解的,不是2-正的,并给出了由此类正线性映射φ生成的纠缠witnessesWφ成为最优的充分必要条件.     

Entanglement of spin waves among four quantum memories

Quantum networks are composed of quantum nodes that interact coherently through quantum channels, and open a broad frontier of scientific opportunities. For example, a quantum network can serve as a 'web' for connecting quantum processors for computation and communication, or as a 'simulator' allowing investigations of quantum critical phenomena arising from interactions among the nodes mediated by the channels. The physical realization of quantum networks generically requires dynamical systems capable of generating and storing entangled states among multiple quantum memories, and efficiently transferring stored entanglement into quantum channels for distribution across the network. Although such capabilities have been demonstrated for diverse bipartite systems, entangled states have not been achieved for interconnects capable of 'mapping' multipartite entanglement stored in quantum memories to quantum channels. Here we demonstrate measurement-induced entanglement stored in four atomic memories; user-controlled, coherent transfer of the atomic entanglement to four photonic channels; and characterization of the full quadripartite entanglement using quantum uncertainty relations. Our work therefore constitutes an advance in the distribution of multipartite entanglement across quantum networks. We also show that our entanglement verification method is suitable for studying the entanglement order of condensed-matter systems in thermal equilibrium.     

Experimental purification of two-atom entanglement

Entanglement is a necessary resource for quantum applications--entanglement established between quantum systems at different locations enables private communication and quantum teleportation, and facilitates quantum information processing. Distributed entanglement is established by preparing an entangled pair of quantum particles in one location, and transporting one member of the pair to another location. However, decoherence during transport reduces the quality (fidelity) of the entanglement. A protocol to achieve entanglement 'purification' has been proposed to improve the fidelity after transport. This protocol uses separate quantum operations at each location and classical communication to distil high-fidelity entangled pairs from lower-fidelity pairs. Proof-of-principle experiments distilling entangled photon pairs have been carried out. However, these experiments obtained distilled pairs with a low probability of success and required destruction of the entangled pairs, rendering them unavailable for further processing. Here we report efficient and non-destructive entanglement purification with atomic quantum bits. Two noisy entangled pairs were created and distilled into one higher-fidelity pair available for further use. Success probabilities were above 35 per cent. The many applications of entanglement purification make it one of the most important techniques in quantum information processing.     

Experimental entanglement distillation and 'hidden' non-locality

Entangled states are central to quantum information processing, including quantum teleportation, efficient quantum computation and quantum cryptography. In general, these applications work best with pure, maximally entangled quantum states. However, owing to dissipation and decoherence, practically available states are likely to be non-maximally entangled, partially mixed (that is, not pure), or both. To counter this problem, various schemes of entanglement distillation, state purification and concentration have been proposed. Here we demonstrate experimentally the distillation of maximally entangled states from non-maximally entangled inputs. Using partial polarizers, we perform a filtering process to maximize the entanglement of pure polarization-entangled photon pairs generated by spontaneous parametric down-conversion. We have also applied our methods to initial states that are partially mixed. After filtering, the distilled states demonstrate certain non-local correlations, as evidenced by their violation of a form of Bell's inequality. Because the initial states do not have this property, they can be said to possess 'hidden' non-locality.