Multiparticle Entangled States Research Articles

Sagnac secret sharing over telecom fiber networks

We report the first Sagnac quantum secret sharing (in three-and four-party implementations) over 1550 nm single mode fiber (SMF) networks, using a single qubit protocol with phase encoding. Our secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber telecom channels and in free-space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. Our experimental data in the three-party implementation show stable (in regards to birefringence drift) quantum secret sharing transmissions at the total Sagnac transmission loop distances of 55-75 km with the quantum bit error rates (QBER) of 2.3-2.4% for the mean photon number micro?= 0.1 and 1.7-2.1% for micro= 0.3. In the four-party case we have achieved quantum secret sharing transmissions at the total Sagnac transmission loop distances of 45-55 km with the quantum bit error rates (QBER) of 3.0-3.7% for the mean photon number micro= 0.1 and 1.8-3.0% for micro?= 0.3. The stability of quantum transmission has been achieved thanks to our new concept for compensation of SMF birefringence effects in Sagnac, based on a polarization control system and a polarization insensitive phase modulator. The measurement results have showed feasibility of quantum secret sharing over telecom fiber networks in Sagnac configuration, using standard fiber telecom components.

Experimental quantum secret sharing using telecommunication fiber

We report quantum secret sharing experiment in telecommunication fiber in five-party implementation. The quantum secret sharing experiment has been based on a single qubit protocol, which has opened the door to practical secret sharing implementation over fiber channels and in free space. The previous quantum secret sharing proposals were based on multiparticle entangled states, difficult in the practical implementation and not scalable. The secret sharing protocol has been implemented in an interferometric fiber optics setup with phase encoding and demonstrated for three, four, and five parties. The experimental setup measurements have shown feasibility and scalability of secure multiparty quantum communication over commercial telecom fiber networks.

Scheme to Implement Optimal Symmetric 1 → 2 Universal Quantum Telecloning Through Cavity-Assisted Interaction

We propose a scheme to implement the optimal symmetric 1 → 2 universal quantum telecloning through cavity-assisted interaction. In our scheme, an arbitrary single atomic state can be telecloned to two single atomic states. And three atoms are trapped in three spatially separated cavities respectively. With a particular multiparticle entangled state acting as a quantum information channel and the trapped single atom acting as a quantum network node for its long-lived internal state, quantum information can be telecloned among nodes and can stored in the nodes.

Generalized parity measurements

Measurements play an important role in quantum computing (QC), by either providing the nonlinearity required for two-qubit gates (linear optics QC), or by implementing a quantum algorithm using single-qubit measurements on a highly entangled initial state (cluster state QC). Parity measurements can be used as building blocks for preparing arbitrary stabilizer states, and, together with 1-qubit gates are universal for quantum computing. Here we generalize parity gates by using a higher dimensional (qudit) ancilla. This enables us to go beyond the stabilizer/graph state formalism and prepare other types of multi-particle entangled states. The generalized parity module introduced here can prepare in one-shot, heralded by the outcome of the ancilla, a large class of entangled states, including GHZ_n, W_n, Dicke states D_{n,k}, and, more generally, certain sums of Dicke states, like G_n states used in secret sharing. For W_n states it provides an exponential gain compared to linear optics based methods.

Probabilistic teleportation of multi-particle partially entangled state

Utilizing the generalized measurement described by positive operator-valued measure, this paper comes up with a protocol for teleportation of an unknown multi-particle entangled (GHZ) state with a certain probability. The feature of the present protocol is to weaken requirement for the quantum channel initially shared by sender and receiver. All unitary transformations performed by receiver are summarized into a formula. On the other hand, this paper explicitly constructs the efficient quantum circuits for implementing the proposed teleportation by means of universal quantum logic operations in quantum computation.

Scheme for probabilistic remotely preparing a multi-particle entangled GHZ state

This paper presents a scheme for probabilistic remote preparation of a three-particle entangled Greenberger- Horne-Zeilinger (GHZ) state via three-particle orthonormal basis projective measurement, and then directly generalize the scheme to multi-particle case. It is shown that by using N pairs of bipartite non-maximally entangled states as the quantum channel and N-particle orthonormal basis projective measurement, the multi-particle remote preparation can be successfully realized with a certain probability.

Multipartitle EPR states†

The Einstein–Podolsky–Rosen (EPR) wavefunction is a two-particle wavefunction that is a simultaneous eigenfunction of the relative coordinate and the centre-of-mass momentum. The Fock space representation of this function is easily obtained as a direct product of an eigenfunction of the relative coordinate and an eigenfunction of the centre-of-mass momentum. Straightforward generalization to an arbitrary number of particles is shown to be feasible, and a classification of multiparticle entangled states is outlined. The relation between entanglement and inseparability is pointed out, and the status of the EPR states within the much broader family of entangled states is emphasized. †Dedicated to Professor Raphael Levine, scholar, man of peace, on his seventieth birthday.

Universal quantum multiple tele-flipping and tele-cloning of an arbitrary qubit

One scheme for universal quantum multiple tele-flipping and tele-cloning of an arbitrary qubit is proposed. Our scheme combines three processes of quantum teleportation, optimal universal quantum flipping and optimal universal quantum cloning, and implements the task by consuming reduced entanglement resources. The key to the realization of this scheme is the construction of the particular 2 ( M + 1 ) -particle entangled state shared by the sender and the spatially separated receivers used as a quantum information channel. The entanglement structure of this multiparticle entangled state is analyzed.

Relaxation and storage of multiparticle entangled states of atoms in a collective thermostat

Multiparticle entangled states that are the generalization of the W class states and can be reduced to Dicke states are considered. The master equation describing the collective decay of atoms in a cavity is derived for the Tavis-Cummings model in the dispersive limit. The entangled states of atoms that are retained in the process of collective decay are found. The scheme for recording and storage of these states in a collective thermostat is presented.

Multiparticle entangled quantum states and modeling of thermodynamic statistical distributions

Thermodynamic equilibrium of a system is considered as a consequence of quantum entanglement of the vacuum state of the system. An explicit mathematical model of multiparticle entangled pure quantum states is developed and analyzed. Within the framework of this model, the measurement process gives rise to probability distributions that exactly correspond to thermal equilibrium of the system in a thermostat.

Two-particle spin entanglement in magnetic Anderson nanoclusters

We investigate the two-particle spin entanglement in magnetic nanoclusters described by the periodic Anderson model. An entanglement phase diagram is obtained, providing an important perspective on a central property of magnetic nanoclusters, namely, the temperature-dependent competition between local Kondo screening and nonlocal Ruderman-Kittel-Kasuya-Yoshida spin ordering. We find that multiparticle entangled states are present for finite magnetic field as well as in the mixed valence regime and away from half filling. Our results emphasize the role of charge fluctuations.

Decay and storage of multiparticle entangled states of atoms in collective thermostat

We derive a master equation describing the collective decay of two-level atoms inside a single mode cavity in the dispersive limit. By considering atomic decay in the collective thermostat, we found a decoherence-free subspace of the multiparticle entangled states of the $W$-like class. We present a scheme for writing and storing these states in collective thermostat.

Diagram rules for a chain of entangled ultracold atoms in optical lattices

The creation of highly entangled state for neutral atoms trapped in optical lattices was reported in a recent experiment by Mandel et al. [Nature 425 (2003) 937]. In the present work, simple diagram rules are given to get the final expression of the multi-particle entangled state created by performing certain multi-particle operations in this experiment. These diagram rules may has potential application in the further experimental test for the nonlocal property of the entangled cluster state.

Efficient scheme to produce multi-particle entanglement with superconducting charge qubits

We propose an efficient scheme to implement high-fidelity multi-particle entangled states in the system consisting of superconducting charge qubits coupled through a single cavity mode. The manipulation is simply to apply specific gate voltages and external magnetic fields threaded through SQUIDs for fixed time. The total number of qubits which can be entangled is limited only from the decoherence time achieved in experiments. The gate operations are based on unconventional geometric phases and thus have built-in fault-tolerant features. The produced multi-qubit entangled states may have many applications.

Scalable multiparticle entanglement of trapped ions

The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are non-interacting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a non-exponential scaling of resources with particle number. Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four-, five-, six-, seven- and eight-particle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a test-bed for theoretical studies of multiparticle entanglement. Independently, 'Greenberger-Horne-Zeilinger' entangled states with up to six ions have been created and analysed in Boulder.

Experimental Analysis of a Four-Qubit Photon Cluster State

Linear-optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences from the usual Greenberger-Horne-Zeilinger (GHZ) state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multiparticle entangled states.

Multiparticle entanglement and the Schrödinger cat state using ground-state coherences

In this paper we show how ground-state coherences and dispersive interactions of single photons with a collective system produces a variety of multiparticle entangled states and mesoscopic superpositions. Further single photons act as a carrier of information and can entangle macroscopic systems and can produce large phase shifts. Our work produces states as considered by Schrödinger in the cat-paradox, though in our case cat is replaced by the collective atomic system.

Toward Heisenberg-limited spectroscopy with multiparticle entangled states.

The precision in spectroscopy of any quantum system is fundamentally limited by the Heisenberg uncertainty relation for energy and time. For N systems, this limit requires that they be in a quantum-mechanically entangled state. We describe a scalable method of spectroscopy that can potentially take full advantage of entanglement to reach the Heisenberg limit and has the practical advantage that the spectroscopic information is transferred to states with optimal protection against readout noise. We demonstrate our method experimentally with three beryllium ions. The spectroscopic sensitivity attained is 1.45(2) times as high as that of a perfect experiment with three non-entangled particles.

Entangled photon states in consecutive nonlinear optical interactions

Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.

SCHEMES FOR REMOTELY PREPARING MULTIPARTITE EQUATORIAL ENTANGLED STATES IN HIGH DIMENSIONS

In this paper, we present two kinds of schemes for remotely preparing multiparticle d-dimensional equatorial entangled states with unit probability. It is found that the first remote state preparation scheme is realized by a multiparticle projective measurement, while the second scheme is achieved by a single particle orthogonal measurement. Each scheme can be perfectly implemented whatsoever the particle number N and the dimension d are.