利用非局域控制非门操作纯化三粒子纠缠态

提出了两套三粒子纠缠态的纯化方案.第一个方案选择部分纠缠GHZ态作为量子通道,利用具有一个控制位和一个靶位的非局域控制非门操作和采用集体么正操作及适当地制备三粒子A,B和C的初始态,可以以最佳几率2|β|2获得最大三粒子纠缠态.第二个方案选择EPR对作为量子通道,通过利用具有一个控制位和两个靶位的非局域控制非门操作和采用集体么正操作及适当地制备三粒子A,B和C的初始态,可以以与第一个方案相同的几率获得最大三粒子纠缠态.两个方案都可以推广到N粒子纠缠态的纯化.     

Dynamics and Recovery of Genuine Multipartite Einstein–Podolsky–Rosen Steering and Genuine Multipartite Nonlocality for a Dissipative Dirac System via the Unruh Effect

The dynamics behaviors of genuine multipartite Einstein–Podolsky–Rosen steering (GMS) and genuine multipartite nonlocality (GMN) are investigated herein, and how the lost GMS and GMN under a mixed decoherence system can be recovered is explored. Explicitly, the decoherence system can be modeled by that a tripartite Werner‐type state suffers from the non‐Markovian regimes and one subsystem of the tripartite is under a non‐inertial frame. The conditions for steerable and nonlocal states can be obtained with respect to the tripartite Werner‐type state established initially. GMS and GMN are very fragile and vulnerable under the influence of the collective decoherence. GMS and GMN will vanish with growing intensity of the Unruh effect and the non‐Markovian reservoir. Besides, all achievable GMN's states are steerable, while not every steerable state (GMS's state) can achieve nonlocality. This means that the steering–nonlocality hierarchy is still tenable and GMN's states are a strict subset of the GMS's states in such a scenario. Subsequently, an available methodology to recover the damaged GMS and GMN is proposed. It turns out that the lost GMS and GMN can be effectively restored, and the ability of GMS and GMN to suppress the collective decoherence can be enhanced.     

Schemes for Splitting Quantum Information via Tripartite Entangled States

In this paper we propose two schemes for quantum information splitting via tripartite entangled states. Explicit protocols for the quantum information splitting of a single qubit state and an arbitrary two-qubit entangled state are illustrated. We also consider the security against certain eavesdropping attacks. Moreover, a generalization of the scheme to multi-particle case is also outlined.     

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement

Schemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.     

Multipartite Quantum Coherence and Distribution under the Unruh Effect

Quantum coherence of the tripartite W state and Greenberger–Horne–Zeilinger (GHZ) state under the Unruh effect are explored based on the model of a two‐level detector qubit coupled to a massless scalar field. The results reveal that Unruh thermal noise really destroys tripartite quantum resources. It is worth mentioning that the quantum coherence of the GHZ state reaches zero in the infinite acceleration limit, but that of the W‐state always remains nonzero. Coherence of the GHZ state displays a sudden death as the coupling parameter grows, while coherence freezing can be witnessed for the W state. It can be concluded that the W state is more robust than the GHZ state against Unruh radiation. Moreover, the related investigation can be expanded to N‐qubit quantum systems and the corresponding analytical solution is obtained. It indicates that the larger number W‐type entangled qubit can be as a better quantum resource for quantum information tasks under the Unruh effect.     

Correlation properties of entangled multiphoton states and Bernstein’s paradox

A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein’s paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.     

Randomized Entangled Mixed States from Phase States

We construct randomized entangled mixed states by using the formalism of phase states for d-dimensional systems (qudits). The randomized entangled mixed states are a special kind of mixed states that exhibit genuine multipartite correlation. Such states are obtained by the application of randomized entangling operators to an arbitrary pair of qudits of a multiqudit system. The study of the entanglement of randomized mixed states is of great importance in quantum computation since any experimental implementation of entangled states in a realistic environment can be made by imperfect entangling gates. We give a brief review of some necessary background about unitary phase operators and phase states of a multi-qudit system. Evolved density matrices arise when qudits of the multi-qudit system interact via a Hamiltonian of Heisenberg type. The randomized entangled states associated with evolved density matrices are derived via the action of an entangling operator on a pair of two qudits {i, j} of the multi-qudit system with some probability p. The randomized entangled mixed states for bipartite, tripartite and multipartite systems are explicitly expressed and their Kraus decomposition properties are discussed.

     

Activating the Violation of Steering Inequality for Two‐Qubit X States

The phenomenon of superactivation of quantum steering, that is, the fact that by combining several copies of the unsteerable quantum state one can get a steerable quantum state, has recently attracted much attention. This property is currently only known for isotropic states, and whether there exists an example other than isotropic states is so far an open question. It is of great importance to learn the activation property of non‐isotropic states. In this paper, it is shown that the violation of the local uncertainty relations (LUR) steering inequality can be activated for two‐qubit X type entangled mixed states. Although the activation phenomenon proven in this paper cannot guarantee the superactivation of steering for two‐qubit X states, it does provide clues for this goal. In addition, previous results indicate that two copies are enough for the superactivation of steering, while the price to pay is a high local dimension, and it is unclear whether superactivation is possible with few copies in low‐dimensional systems such as two‐qubit systems. By providing examples of activation of LUR steering inequality with two copies in a two‐qubit system, the work may open a potential way to the solution of this question.     

Reversible combination of inequivalent kinds of multipartite entanglement

We present a family of tripartite entangled states that, in an asymptotical sense, can be reversibly converted into Einstein-Podolsky-Rosen (EPR) states, shared by parties B and C, and tripartite Greenberger-Horne-Zeilinger (GHZ) states. Thus we show that a bipartite and a genuine tripartite entanglement can be reversibly combined in a tripartite state. For such states the corresponding fractions of GHZ and EPR states represent a complete quantification of their (asymptotical) entanglement resources. More generally, we show that AB, AC, and BC EPR entanglement and GHZ entanglement can be reversibly combined in a single tripartite state. Finally, we generalize this result to any number of parties.     

Quantum cobwebs: Universal entangling of quantum states

Entangling an unknown qubit with one type of reference state is generally impossible. However, entangling an unknown qubit with two types of reference states is possible. To achieve this, we introduce a new class of states called zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and study their salient features. Using shared-ZSA states, local operations and classical communication, we give a protocol for creating multipartite entangled states of an unknown quantum state with two types of reference states at remote places. This provides a way of encoding an unknown pure qubit state into a multiqubit entangled state.     

Circular Controlled Quantum Teleportation by a Genuine Seven-qubit Entangled State

A scheme of circular controlled quantum teleportation, which is a novel version of bidirectional controlled quantum teleportation, is proposed using a specific genuine seven-qubit entangled state as quantum channel, and then it is generalized to the scene with a general genuine seven-qubit entangled state as channel. This means that with the control of the supervisor Daniel while Alice teleportates an unknown qubit state to Bob, Bob can also teleportate an unknown qubit state to Charlie and Charlie can also teleportate an unknown qubit state to Alice circularly, simultaneously. Compared with the BCQT schemes proposed before, the intrinsic efficiency of our scheme is optimal.

     

Quantum teleportation using entangled 3-qubit states and the ‘magic bases’

We study quantum teleportation of single qubit information state using 3-qubit general entangled states. We propose a set of 8 GHZ-like states which gives (i) standard quantum teleportation (SQT) involving two parties and 3-qubit Bell state measurement (BSM) and (ii) controlled quantum teleportation (CQT) involving three parties, 2-qubit BSM and an independent measurement on one qubit. Both are obtained with perfect success and fidelity and with no restriction on destinations (receiver) of any of the three entangled qubits. For SQT, for each designated one qubit which is one of a pair going to Alice, we obtain a magic basis containing eight basis states. The eight basis states can be put in two groups of four, such that states of one group are identical with the corresponding GHZ-like states and states of the other differ from the corresponding GHZ-like states by the same phase factor. These basis states can be put in two different groups of four-states each, such that if any entangled state is a superposition of these with coefficients of each group having the same phase, perfect SQT results. Also, for perfect CQT, with each set of given destinations of entangled qubits, we find a different magic basis. If no restriction on destinations of any entangled qubit exists, three magic semi-bases, each with four basis states, are obtained, which lead to perfect SQT. For perfect CQT, with no restriction on entangled qubits, we find four magic quarter-bases, each having two basis states. This gives perfect SQT also. We also obtain expressions for co-concurrences and conditional concurrences.     

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.)     

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, the correlations of the tripartite W‐type states based on bipartite quantum resources are investigated. The inter‐relations among the degree of coherence, concurrence, Bell nonlocality, and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser–Horne–Shimony–Holt inequality) states for the two‐qubit subsystems derived from the tripartite W‐type states, exact lower and upper boundaries of the degree of coherence versus concurrence are obtained. Interestingly, exact relation among the degree of coherence, concurrence, and purity is obtained. Moreover, coherence is also closely related to entanglement in two specific scenarios: the tripartite W‐type state under decoherence and a practical system for a renormalized spin‐1/2 Heisenberg model.     

New Properties of the Wigner Function of the Tripartite Entangled State

For entangled three particles one should treat their wave function as a whole, there is no physical meaning talking about the wave function (or Wigner function) for any one of the tripartite, therefore thinking of the entangled Wigner function (Wigner operator) is of necessity, we introduce the entangled Wigner operator related to a pair of mutually conjugate tripartite entangled state representations and discuss some of its new properties, such as the trace product rule, the size of an entangled quantum state and the upper bound of the three-mode Wigner function. Deriving wave function from its corresponding tripartite entangled Wigner function is also presented. Those new properties of the tripartite entangled Wigner function play significant role in quantum physics because they provide us deeper insight into the shape of quantum states.     

On precession of entangled spins in a strong laser field

A dynamics of the entanglement under an environmental influence is modelled by a bound state composed of two heavy particles interacting with a strong laser. Adopting the semiclassical attitude, a trajectory of the bound state’s center-of-mass is found from the Newton equations solved beyond the dipole approximation and taking into account the magnetic field effect. At the same time the dynamics of constituent spins under the laser coupling is studied quantum mechanically solving the nonrelativistic von Neumann equation with the effective Hamiltonian determined by the bound state’s classical trajectory. Based on the solution, the effects of an intense linearly polarized monochromatic plane wave on the precession of entangled spins are discussed for a specific kind of mixed initial states including a family of maximally entangled Werner states. The text was submitted by the authors in English.     

Detecting Tripartite Steering via Quantum Entanglement

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The “complex cost” of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states.     

Nonadditivity of bipartite distillable entanglement follows from a conjecture on bound entangled Werner states

Assuming the validity of a conjecture given by DiVincenzo et al. [Phys. Rev. A 61, 062312 (2000)] and by Dür et al. [Phys. Rev. A 61, 062313 (2000)], we show that the distillable entanglement for two bipartite states, each of which individually has zero distillable entanglement, can be nonzero. We show that this also implies that the distillable entanglement is not a convex function. Our example consists of the tensor product of a bound entangled state based on an unextendible product basis with an entangled Werner state which lies in the class of conjectured undistillable states.     

Generation of macroscopic entangled coherent states with large Josephson junctions

We propose a simple and experimental architecture to generate macroscopic entanglement in a solid system which consists of two large Josephson junctions and a flux qubit. Through quantum measuring of flux qubit, entangled coherent states of two large Josephson junctions are obtained. The concurrence of entangled coherent states can be accommodated by adjusted systematic parameters. We also give a brief discussion on the experimental feasibility of this proposal.     

Resource-Efficient Direct Entanglement Measurement of Werner State with Hybrid Spin-Photon Interaction System

We propose two resource-efficient schemes of direct entanglement measurement of two-qubit Werner states via hybrid interaction system with nitrogen-vacancy (NV) center coupled to micro-cavity. Based on the unconventional encoding mode on auxiliary qubits, our physical unit can realize the hybrid controlled phase gate and controlled-NOT gate between spin and polarization qubits. Utilizing only one copy of initial entangled state, we implement direct concurrence measurement of spin Werner states in NV centers and polarization Werner states of single photons. Both schemes can be transformed into remote ones with the initial entangled states possessed by spatially separated participants. Experimental feasibility analyses indicate that the presented schemes have reliable performance in the current available experimental conditions.