Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements

Entanglement plays an important role in quantum information science, especially in quantum communications. Here we present an efficient entanglement concentration protocol (ECP) for nonlocal atom systems in the partially entangled W-class states, using the single-photon input-output process regarding low-Q cavity and linear optical elements. Compared with previously published ECPs for the concentration of non-maximally entangled atomic states, our protocol is much simpler and more efficient as it employs the Faraday rotation in cavity quantum electrodynamics (QED) and the parameter-splitting method. The Faraday rotation requires the cavity with low-Q factor and weak coupling to the atom, which makes the requirement for entanglement concentration much less stringent than the previous methods, and achievable with current cavity QED techniques. The parameter-splitting method resorts to linear-optical elements only. This ECP has high efficiency and fidelity in realistic experiments, and some imperfections during the experiment can be avoided efficiently with currently available techniques.     

Entanglement in non-Hermitian quantum theory

Entanglement is one of the key features of quantum world that has no classical counterpart. This arises due to the linear superposition principle and the tensor product structure of the Hilbert space when we deal with multiparticle systems. In this paper, we will introduce the notion of entanglement for quantum systems that are governed by non-Hermitian yet PT-symmetric Hamiltonians. We will show that maximally entangled states in usual quantum theory behave like non-maximally entangled states in PT-symmetric quantum theory. Furthermore, we will show how to create entanglement between two PT qubits using non-Hermitian Hamiltonians and discuss the entangling capability of such interaction Hamiltonians that are non-Hermitian in nature.     

Coherent-state qubits: entanglement and decoherence

Arbitrary superpositions of any two optical coherent states are investigated as realizations of qubits for quantum information processing. Decoherence of these coherent-state qubits is described in detail, and visualized using a suitable adaptive Bloch-sphere. The entanglement that can be created by a beam splitter from these states is quantified, and its decoherence behavior is analyzed.Received: 13 May 2004, Published online: 10 August 2004PACS: 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.) - 03.67.-a Quantum information     

Entanglement Swapping for Cluster-Class States and Its Applications in Quantum Information Processing

Entanglement swapping for four-qubit cluster-class states is studied. It is shown that a four-qubit cluster state (maximally entangled) can be obtained with a certain probability from two four-qubit cluster-class states by entanglement swapping. The probability is related to the smallest superposition coefficient of the cluster-class states (when all the moduli of amplitudes are equivalent, they are the usual cluster states and the probability hits to one). Two examples for the applications of the entanglement swapping are also presented. One is quantum teleportation of an arbitrary two-qubit state via a quantum repeater, in which the success probability can be improved by the entanglement swapping when the quantum channels are general cluster-class states (partially entangled). The other is quantum key distribution, in which a secret random sequence of bits (a “key”) can be efficiently established between two distant parties by the entanglement swapping of two groups of cluster states.     

Experimental detection of qubit-ququart pseudo-bound entanglement using three nuclear spins

In this work, we experimentally created and characterized a class of qubit-ququart PPT (positive under partial transpose) entangled states using three nuclear spins on an nuclear magnetic resonance (NMR) quantum information processor. Entanglement detection and characterization for systems with a Hilbert space dimension $\ge 2?3$ is nontrivial since there are states in such systems which are both PPT as well as entangled. The experimental detection scheme that we devised for the detection of qubit-ququart PPT entanglement was based on the measurement of three Pauli operators with high precision, and is a key ingredient of the protocol in detecting entanglement. The family of PPT-entangled states considered in the current study are incoherent mixtures of five pure states. All the five states were prepared with high fidelities and the resulting PPT entangled states were prepared with mean fidelity ≥ 0.95. The entanglement thus detected was validated by carrying out full quantum state tomography (QST).     

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.     

Demonstration of Quantum Entanglement Control Using Nuclear Magnetic Resonance

With the two forms of the quantum entanglement control, the quantum entanglement swapping and preservation are demonstrated in a three-qubit nuclear magnetic resonance quantum computer. The pseudopure state is prepared to represent the quantum entangled states through macroscopic signals. Entanglement swapping is directly realized by a swap operation. By controlling the interactions between the system and its environment,we can preserve an initial entangled state for a longer time. The experimental results are in agreement with the experiment.     

Cloning the entanglement of a pair of d-dimensional quantum systems

We derive a quantum cloning machine that maximizes the entanglement of formation of the two copies of any maximally entangled input state, while preserving the separability of all unentangled input states. In addition, it is proven to optimally duplicate the entanglement of formation of all isotropic input states. For large d, the cloning machine behaves classically and outperforms a local entanglement cloner, studied for comparison. The text was submitted by the authors in English.     

Controlled teleportation of an arbitrary n-qudit state using nonmaximally entangled GHZ states

In this paper, we explicitly present a general scheme for controlled quantum teleportation of an arbitrary multi-qudit state with unit fidelity and non-unit successful probability using d-dimensional nonmaximally entangled GHZ states as the quantum channel and generalized d-dimensional Bell states as the measurement basis. The expression of successful probability for controlled teleportation is present depending on the degree of entanglement matching between the quantum channel and the generalized Bell states. And the formulae for the selection of operations performed by the receiver are given according to the results measured by the sender and the controller.      

A tentative approach to entanglement measures for a system of a three-level atom interacting with a quantized cavity-field

In this paper, an entanglement measure due to quasi-mutual entropy from initially entangled mixed states of a three-level atom interacting with a single cavity field is introduced. Detailed analytical and explicit expressions are given taking into account an arbitrary form of the intensity-dependent coupling. Despite its simplicity the model exhibits a very broad range of intricate physical effects and it is widely used in quantized theories of laser. We show that quantum revivals are possible for a broad continuous range of physical parameters in the case of initial coherent states. Entanglement degree effects are shown to be very sensitive to the initial state of the system. Numerical calculations under current experimental conditions are taken into account and it is found that the intensity-dependent coupling changes the general features dramatically.Received: 2 June 2003, Published online: 26 August 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.) - 03.67.Hk Quantum communication - 42.65.-k Nonlinear optics - 32.80.Rm Multiphoton ionization and excitation to highly excited states (e.g., Rydberg states)     

One-and-a-Half Quantum de Finetti Theorems

When n − k systems of an n-partite permutation-invariant state are traced out, the resulting state can be approximated by a convex combination of tensor product states. This is the quantum de Finetti theorem. In this paper, we show that an upper bound on the trace distance of this approximation is given by , where d is the dimension of the individual system, thereby improving previously known bounds. Our result follows from a more general approximation theorem for representations of the unitary group. Consider a pure state that lies in the irreducible representation of the unitary group U(d), for highest weights μ, ν and μ + ν. Let ξ_μ be the state obtained by tracing out U _ν. Then ξ_μ is close to a convex combination of the coherent states , where and is the highest weight vector in U _μ. For the class of symmetric Werner states, which are invariant under both the permutation and unitary groups, we give a second de Finetti-style theorem (our “half” theorem). It arises from a combinatorial formula for the distance of certain special symmetric Werner states to states of fixed spectrum, making a connection to the recently defined shifted Schur functions [1]. This formula also provides us with useful examples that allow us to conclude that finite quantum de Finetti theorems (unlike their classical counterparts) must depend on the dimension d. The last part of this paper analyses the structure of the set of symmetric Werner states and shows that the product states in this set do not form a polytope in general.     

Entanglement Swapping Transform Rule of Entangled Wigner Operators

For mixed input fields quantum information processing, it is very convenient to investigate a specified protocol by employ quasi-probability functions and characteristic functions in phase space. In this work, considering a nonlocal swapping operation labelled by  $\hat{E}_{s}$ , we derive the entanglement swapping transform rule for entangled Wigner operators. The same rule can be obtained by implementing this nonlocal swapping operation via two entangled pairs channels. And then we apply this rule to examine how does the Wigner function for output states change to demonstrate the entanglement swapping. As a result, this transform rule can be utilized to investigate swapping operation for any two-body entangled system.     

Separability criterion for quantum effects

Entanglement of quantum states is absolutely essential for modern quantum sciences and technologies. It is natural to extend the notion of entanglement to quantum observables dual to quantum states. For quantum states, various separability criteria have been proposed to determine whether a given state is entangled. In this Letter, we propose a separability criterion for specific quantum effects (binary observables) that can be regarded as a dual version of the Bell–Clauser–Horne–Shimony–Holt (Bell–CHSH) inequality for quantum states. The violation of the dual version of the Bell–CHSH inequality is confirmed by using IBM's cloud quantum computer. As a consequence, the violation of our inequality rules out the maximal tensor product state space, that satisfies information causality and local tomography. As an application, we show that an entangled observable which violates our inequality is useful for quantum teleportation.     

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous‐variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous‐variable entanglement and show how to make it. The members of a family of multi‐mode states are found to be truly multi‐party entangled with respect to all their modes. These states also violate multi‐party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi‐party continuous‐variable entanglement. Various quantum communication protocols based on the continuous‐variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous‐variable entanglement swapping. We highlight the similarities and differences between continuous‐variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi‐party generalization of quantum teleportation. This so‐called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no‐cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase‐insensitive amplifier and beam splitters.     

Entanglement or separability: the choice of how to factorize the algebra of a density matrix

Quantum entanglement has become a resource for the fascinating developments in quantum information and quantum communication during the last decades. It quantifies a certain nonclassical correlation property of a density matrix representing the quantum state of a composite system. We discuss the concept of how entanglement changes with respect to different factorizations of the algebra which describes the total quantum system. Depending on the considered factorization a quantum state appears either entangled or separable. For pure states we always can switch unitarily between separability and entanglement, however, for mixed states a minimal amount of mixedness is needed. We discuss our general statements in detail for the familiar case of qubits, the GHZ states, Werner states and Gisin states, emphasizing their geometric features. As theorists we use and play with this free choice of factorization, which for an experimentalist is often naturally fixed. For theorists it offers an extension of the interpretations and is adequate to generalizations, as we point out in the examples of quantum teleportation and entanglement swapping.     

Entanglement Dynamics of Electrons and Photons

Entanglement is a fundamental feature of quantum theory as well as a key resource for quantum computing and quantum communication, but the entanglement mechanism has not been found at present. We think when the two subsystems exist interaction directly or indirectly, they can be in entanglement state. such as, in the Jaynes-Cummings model, the entanglement between the atom and the light field comes from their interaction. In this paper, we have studied the entanglement mechanism of electron-electron and photon-photon, which are from the spin-spin interaction. We found their total entanglement states are relevant both space state and spin state. When two electrons or two photons are far away, their entanglement states should be disappeared even if their spin state is entangled.     

Entanglement, Hubbard Model, and Symmetries

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding, and quantum teleportation. We use the requirements for a state in the Hilbert space C ² C ² to be entangled to find when states evolving under the two-point Hubbard model become entangled. We also investigate the connection of entanglement and discrete symmetries of the two-point Hubbard model. Furthermore we discuss the inclusion of phonon coupling.     

Maximal entanglement of bipartite spin states in the context of quantum algebra

In the framework of the U _q (su(2)) quantum algebra, we investigate the entanglement properties of two-spin systems, of arbitrary spins j ₁ and j ₂, defined in an entanglement of deformed spin coherent states of each of the spins. We derive the amount of entanglement and we give conditions under which bipartite entangled states become maximally entangled. Using these conditions, we construct a large class of Bell states for any choices of the parameters that specify the spin coherent states.