Schmidt modes and entanglement

Motivated by their frequent use in quantum mechanical studies of entanglement, we give a brief overview of Schmidt modes and Schmidt decompositions of two-particle wave functions. We discuss methods of their derivation and include a little-known approach used in the original work by E. Schmidt [Math. Annalen, 63 (1906), 433]. This employs the bipartite wave function itself rather than the more complicated two-party reduced density matrix. As an illustration, Schmidt modes for two-photon polarisation qutrits are derived in a general form. The derivation is accompanied by a series of simple examples with special choices of parameters. Relationships between Schmidt modes, polarisation Stokes vectors and entanglement are also discussed.     

Exact formula of the distribution of Schmidt eigenvalues for dynamical formation of entanglement in quantum chaos

The exact formula of the one-level distribution of the Schmidt eigenvalues is obtained for dynamical formation of entanglement in quantum chaos. The formula is based on the random matrix theory of the fixed-trace ensemble, and is derived using the theory of the holonomic system of differential equations. We confirm that the formula describes the universality of the distribution of the Schmidt eigenvalues in quantum chaos.     

Macroscopic entanglement by entanglement swapping

We present a scheme for entangling two micromechanical oscillators. The scheme exploits the quantum effects of radiation pressure and it is based on a novel application of entanglement swapping, where standard optical measurements are used to generate purely mechanical entanglement. The scheme is presented by first solving the general problem of entanglement swapping between arbitrary bipartite Gaussian states, for which simple input-output formulas are provided.     

Comparative analysis of entanglement measures based on monogamy inequality

We evaluate the monogamy inequality for symmetric, non-symmetric pure states of importance in terms of squared concurrence, squared entanglement of formation, squared negativity of partial transpose and compare the corresponding tangles. We show that though concurrence and concurrence tangle are zero for two special classes of mixed entangled states, both negativity tangle and entanglement of formation(EOF) tangle turn out to be non-zero. A comparison of different tangles is carried out in each case and it is shown that while the concurrence tangle captures the genuine multiqubit entanglement in N-qubit pure states with N distinct spinors(containing GHZ and superposition of W-, obverse W states)either negativity tangle or EOF tangle is to be used as a better measure of entanglement in the W-class of states with two distinct spinors and in the special classes of mixed multiqubit states.     

Recovery of entanglement lost in entanglement manipulation

When an entangled state is transformed into another one with probability one by local operations and classical communication, the quantity of entanglement decreases. This Letter shows that entanglement lost in the manipulation can be partially recovered by an auxiliary entangled pair. As an application, a maximally entangled pair can be obtained from two partially entangled pairs with probability one. Finally, this recovery scheme reveals a fundamental property of entanglement relevant to the existence of incomparable states.     

Polarization entanglement purification using spatial entanglement

We present a scheme for entanglement purification with linear optics that works for currently available parametric down-conversion sources, in contrast to a previous scheme [J. W. Pan, Nature (London) 410, 1067 (2001)]] that relied on ideal single-pair sources. The present scheme makes use of spatial entanglement in order to purify polarization entanglement. Surprisingly, spatial entanglement as an additional resource also leads to a substantial improvement in entanglement output compared to the previous scheme.     

两腔级联纠缠增强的理论分析

高纠缠度的纠缠源是实现高保真度量子信息传输与处理的保障,因为受到光学元器件自身性能不完美的限制,通过有效的操控手段来提高光场的纠缠度是十分必要的.连续变量Einstein-Podolsky-Rosen纠缠态光场可以利用工作在阈值以下的非简并光学参量放大器来获得.将两个非简并光学参量放大器级联,可以利用第二个光学腔来操控第一个光学腔输出的纠缠态光场,在一定条件下实现光场的纠缠增强.本文通过理论分析设计出两种光学腔级联的实验系统,其中,纠缠产生装置采用具有三共振结构的半整块驻波腔,输出到目前为止世界上单腔获得两组份纠缠态光场纠缠度的最高值,操控光学腔采用驻波腔或四镜环形腔的结构.详细对比分析了不同结构的操控腔对纠缠增强效果的影响,得出利用不同腔形作为操控腔的最佳实验方案.同时分析了级联腔输出光场的纠缠度随不同物理参量的变化关系,得出进一步优化的最佳实验系统参量,为实验获得更高纠缠度的纠缠态光场提供了依据.     

Modular entanglement

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.     

Robust entanglement

It is common belief among physicists that entangled states of quantum systems lose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca⁺ ions and observe robust entanglement lasting for more than 20 s.     

量子纠缠信令网Poisson生存模型及保真度分析

量子信令态在传输过程中,由于环境影响产生退相干,造成信令损伤,从而会对构建高生存性的量子纠缠信令网产生影响. 为分析所造成的影响,建立了自然灾害下的量子信令网Poisson损伤模型. 首先,根据信令保真度定义了灾害级数;其次,提出信令态平均损伤量子比特数,并给出信令网生存函数;最后,研究了信令损伤的修复策略并进行仿真. 仿真结果表明,灾害级数的增加会大大降低信令网生存性,而增加信令转接点数和控制信令损伤上限可改善生存性,且该修复策略循环次数少,并可将信令态的保真度由0.6快速提高到0.9,信令网的生存函数由0.4提高到0.9. 关键词： 量子通信 量子信令网 保真度 生存函数     

Achromatic Schmidt corrector plates

Two types of achromatic Schmidt corrector plate are described; both give an on-axis Strehl number S 0.8 over an extended wavelength region. It is found that this specification can only be achieved by combining a positive and a negative plate and by restricting the speed ratio D/N³ of the system. The theory is illustrated by numerical examples.     

Collective coordinates as open systems: (II). Time-scale for pure-state propagation

In the frame of a general master equation, we investigate the condition for the propagation of pure-state wave packets conditioned to the gain-loss competition between the different components. If a perturbative approach is adopted, it is shown that the hamiltonian type of evolution is destroyed within the microscopic time-scale, thus inhibiting the possibility of simulating the motion via a frictional Schrödinger equation as frequently undertaken.     

相位阻尼通道下初始纠缠对纠缠演化的影响

研究了在非惯性系中相位阻尼通道下初始纠缠对纠缠演化的影响.结果发现:与振幅阻尼通道情况不同,当态参数不同而初始纠缠相同时,纠缠演化曲线重合.当Unruh单粒子态包含左右成分时,比只包含右成分时量子消相干现象更加严重,较早地出现了纠缠死亡现象,并且纠缠死亡时刻与初始纠缠无关.     

Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Continuous-variable quantum key distribution(CVQKD) protocols with entanglement in the middle(EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However,in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.     

Nonlinear entanglement witnesses

Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.     

Multistage entanglement swapping

We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements: one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an entangled state, as characterized by an entanglement witness. The experiment represents an important step towards a full quantum repeater where multiple entanglement swapping is a key ingredient.