Multipartite Entangled States Research Articles

New approach for constructing generalized entangled state representations

We propose a new approach for constructing generalized entangled state representation of continuum variables, i.e., we introduce some normally ordered Gaussian-form operators, representing the completeness relation (integration of unity), and the resolution of unity leads to projection operator of entangled state vector whose explicit form in Fock space can be derived. The technique of integration within an ordered product (IWOP) of operators is essential in our discussions. For examples, we derive the entangled state representation for two particles with different masses and a kind of multipartite entangled state representation.

Experimental Determination of Multipartite Entanglement with Incomplete Information

Multipartite entanglement is very poorly understood despite all the theoretical and experimental advances of the last decades. Preparation, manipulation and identification of this resource is crucial for both practical and fundamental reasons. However, the difficulty in the practical manipulation and the complexity of the data generated by measurements on these systems increase rapidly with the number of parties. Therefore, we would like to experimentally address the problem of how much information about multipartite entanglement we can access with incomplete measurements. In particular, it was shown that some types of pure multipartite entangled states can be witnessed without measuring the correlations [M. Walter et al., Science 340, 1205 (2013)] between parties, which is strongly demanding experimentally. We explore this method using an optical setup that permits the preparation and the complete tomographic reconstruction of many inequivalent classes of three- and four-partite entangled states, and compare complete versus incomplete information. We show that the method is useful in practice, even for non-pure states or non ideal measurement conditions.

The New Multipartite Squeezing Operator and Some of its Properties

In this paper, we introduce a pair of mutually conjugate multipartite entangled state representations for defining the squeezing operator of entangled multipartite Sn(λ) which involves an n-mode bosonic operator realization of the SU(1,1) Lie algebra. This operator squeezes the multipartite entangled state in a natural way. We discuss the transform properties of aj and \(a_{j}^{\dagger }\) under the operation of Sn(λ) and derive the interaction Hamiltonian which can generate such an evolution. In addition, the corresponding multipartite squeezed vacuum state |λ〉 is obtained. Based on this, the variances of the n-mode quadratures in |λ〉 are evaluated and the violation of the Bell inequality for |λ〉 is examined by using the formalism of Wigner representation.

Generations of N-atom GHZ state and $$2^n$$ 2 n -atom W state assisted by quantum dots in optical microcavities

Multipartite entangled state plays a crucial role in quantum applications. We propose theoretical schemes to generate entanglements among several trapped atoms with the help of quantum dots in single-side optical microcavities. In the first scheme, a basic architecture will be built to produce arbitrary N-atom GHZ state by using only one auxiliary photon. Moreover, using a photon state with multiple modes, we can realize $$2^n$$2n-atom W state. All these schemes are insensitive to the variation of the atom---photon coupling rates and are also right for remotely trapped atoms by using the photonic transmissions, local quantum operations, and classical channel. Simulations show that our schemes are faithful and available with present physical techniques.

Fast Generation of GHZ States with Bose—Einstein Condensate in a Cavity* *Supported by the National Fundamental Research Program of China under Grant No. 2013CB921804, the Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT1243, and the Natural Science Foundation of Anhui Province under Grant No. 1408085MA20

It is shown that strong coupling of Bose—Einstein condensates to an optical cavity can be realized experimentally. With an additional driven microwave field, we show that a highly nonlinear coupling among atoms in a Bose—Einstein condensate can be induced with the assistance of the cavity mode. With such interaction, we can investigate the generation of many body entangled states. In particularly, we show that multipartite entangled GHZ states can be obtained in such architecture with current available techniques.

Quantum scheme for secret sharing based on local distinguishability

In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under {\em restricted local operation and classical communication}. Based on this local distinguishability analysis we propose a new scheme for quantum secret sharing (QSS). Our QSS scheme is quite general and cost efficient compared to other schemes. In our scheme no joint quantum operation is needed to reconstruct the secret. We also present an interesting $(2,n)$-threshold QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This QSS scheme is quite uncommon, as most $(k,n)$-threshold schemes have the restriction $k\geq\lceil\frac{n}{2}\rceil$.

Decoherence effects on the nonlocality of symmetric states

The observation of the non-local properties of multipartite entangled states is of great importance for quantum information protocols. Such properties, however, are fragile and may not be observed in the presence of decoherence exhibited by practical physical systems. In this work, we investigate the robustness of the non-locality of symmetric states experiencing phase and amplitude damping, using suitable Bell inequalities based on an extended version of Hardy's paradox. We derive thresholds for observing non-locality in terms of experimental noise parameters, and demonstrate the importance of the choice of the measurement bases for optimizing the robustness. For $W$ states, in the phase damping case, we show that this choice can lead to a trade-off between obtaining a high violation of the non-local test and optimal robustness thresholds; we also show that in this setting the non-locality of $W$ states is particularly robust for a large number of qubits. Furthermore, we apply our techniques to the discrimination of symmetric states belonging to different entanglement classes, thus illustrating their usefulness for a wide range of practical quantum information applications.

Detection of quantum steering in multipartite continuous-variable Greenberger-Horne-Zeilinger–like states

The multipartite entangled state has drawn broad attention for both foundations of quantum mechanics and applications in quantum information processing. Here, we study the spatially separated $N$-partite continuous-variable Greenberger-Horne-Zeilinger--like states, which can be produced by a linear optical network with squeezed light and $N\ensuremath{-}1$ beamsplitters. We investigate the properties of multipartite Einstein-Podolsky-Rosen steering possessed by those states, and find that the steering of a given quantum mode is allowed when not less than half of the modes within the states take part in the steering group. This is certified by the detection of the correlation between position and momentum quadratures of the steered mode and a combination of quadratures of other modes inside the steering group. The steering is evidenced by the high correlation where the steering group can infer the quadratures of the steered mode to high precision, i.e., below the quantum limit for the position and momentum quadratures of the steered quantum mode. We also examine the influence of inefficiency on the multipartite steering, and derive the threshold of the loss tolerance. Furthermore, we discuss the collective $N$-partite steering induced by the asymmetric loss on beams, which exists when a given quantum mode can only be steered by all the remaining $N\ensuremath{-}1$ modes collaboratively. The present multipartite steering correlation may have potential applications in certain quantum information tasks where the issue of trust is important, such as one-sided device-independent quantum secret sharing.

True multipartite entanglement Hardy test

Quantum mechanics allows systems to be entangled with each other, which results in stronger than classical correlations. Many methods of identifying entanglement have been proposed over years, most of which are based on violating some statistical inequalities. In this work we extend the idea due to Hardy, in which entanglement is not identified with use of statistical inequalities, but by simultaneous satisfaction of certain conditions. We show that the new variant of the Hardy paradox relying on marginal probabilities can be resolved only by true multipartite entangled states. Also, the state resolving this paradox for given local measurements is pure and unique in case of qubit collections.

Generating genuine multipartite entanglement via X Y-interaction and via projective measurements

We have studied the generation of multipartite entangled states for the superconducting phase qubits. The experiments performed in this direction have the capacity to generate several specific multipartite entangled states for three and four qubits. Our studies are also important as we have used a computable measure of genuine multipartite entanglement whereas all previous studies analyzed certain probability amplitudes. As a comparison, we have reviewed the generation of multipartite entangled states via von Neumann projective measurements.

Beam Splitter-Mediated Quantum Information Processing Employing Momentum States of the Neutral Atoms

We propose various schemes for the generation and manipulation of a variety of atomic external transverse momentum states. The fundamental ingredient of all such states is a simple bipartite cavity field-atomic momentum entangled state generated through second order, off-resonant Bragg diffraction of the neutral two-level atoms. Further multipartite entangled state engineering and manipulation including Bell, GHZ, Dicke and W-state production, remote state-assisted entanglement swapping, and teleportation of a cavity field superposition as well as the entanglement onto atomic momentum states are carried out by simultaneously projecting the cavity field(s) over symmetric beam splitter(s). It is further discussed that generation and manipulation of such decoherence resistant momentum states is quite feasible under prevailing experimental research scenario in cavity QED.

Protocols of quantum key agreement solely using Bell states and Bell measurement

Two protocols of quantum key agreement (QKA) that solely use Bell state and Bell measurement are proposed. The first protocol of QKA proposed here is designed for two-party QKA, whereas the second protocol is designed for multi-party QKA. The proposed protocols are also generalized to implement QKA using a set of multi-partite entangled states (e.g., 4-qubit cluster state and $$\Omega $$ state). Security of these protocols arises from the monogamy of entanglement. This is in contrast to the existing protocols of QKA where security arises from the use of non-orthogonal state (non-commutativity principle). Further, it is shown that all the quantum systems that are useful for implementation of quantum dialogue and most of the protocols of secure direct quantum communication can be modified to implement protocols of QKA.

Distillation of multipartite entanglement by local filtering operations

In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach $1.0$ for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.

Generation of multipartite entangled coherent states via a superconducting charge qubit

In this paper, we propose a method to generate multipartite entangled coherent states (MECS) using a multi-mode superconducting cavity containing an SQUID-based charge qubit. After the projective measurement of simple charge states, MECS representing nonlocal electromagnetic fields of cavity modes have been generated. Furthermore, we investigate the nonlocal properties of the generated MECS by constructing the new concurrence-like entanglement based on the Bell–Klyshko argument.

Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement.

We demonstrate entangling quantum gates within a chain of five trapped ion qubits by optimally shaping optical fields that couple to multiple collective modes of motion. We individually address qubits with segmented optical pulses to construct multipartite entangled states in a programmable way. This approach enables high-fidelity gates that can be scaled to larger qubit registers for quantum computation and simulation.

Generation of multimode squeeze operators and multipartite entangled states for continuous variables

A scheme is presented for generating unitarily multimode field squeezing, cluster entanglement, and Greenberger-Horne-Zeilinger (GHZ) entanglement via cavity quantum electrodynamics. Through a suitable laser system, we are able to engineer a squeeze field operator decoupled from the atomic degrees of freedom, yielding a large squeeze parameter proportional to the number of atoms. The physical mechanism is attributed to the multiple four-photon processes and the dispersive atom-cavity-field interaction in large detuning systems.

Measures of genuine multipartite entanglement for graph states

Graph states are special multipartite entangled states that have been proven useful in a variety of quantum information tasks. We address the issue of characterizing and quantifying the genuine multipartite entanglement of graph states up to eight qubits. The entanglement measures used are the geometric measure, the relative entropy of entanglement, and the logarithmic robustness, have been proved to be equal for the genuine entanglement of a graph state. We provide upper and lower bounds as well as an iterative algorithm to determine the genuine multipartite entanglement.

Preparation of multipartite entangled states used for quantum information networks

The preparation of multipartite entangled states is the prerequisite for exploring quantum information networks and quantum computation. In this paper, we review the experimental progress in the preparation of cluster states and multi-color entangled states with continuous variables. The preparation of lager scale multipartite entangled state provide valuable quantum resources to implement more complex quantum informational tasks.

Multipartite entanglement and few-body Hamiltonians

We investigate the possibility to obtain higly multipartite-entangled states as non-degenerate eigenstates of Hamiltonians that involve only short-range and few-body interactions. We study small-size systems (with a number of qubits ranging from three to five) and search for Hamiltonians with a maximally multipartite entangled state (MMES) as a non-degenerate eigenstate. We then find conditions, including bounds on the number of coupled qubits, to build a Hamiltonian with a Greenberger–Horne–Zeilinger (GHZ) state as a non-degenerate eigenstate. We finally comment on possible applications.

Universal gates for transforming multipartite entangled Dicke states

We determine the minimal number of qubits that it is necessary to have access to in order to transform Dicke states into other Dicke states. In general, the number of qubits in Dicke states cannot be increased via transformation gates by accessing only a single qubit, in direct contrast to other multipartite entangled states such as GHZ, W and cluster states. We construct a universal optimal gate which adds spin-up qubits or spin-down qubits to any Dicke state by minimal access. We also show the existence of a universal gate which transforms any size of Dicke state as long as it has access to at least the required number of qubits. Our results have important consequences for the generation of Dicke states in physical systems such as ion traps, all-optical setups and cavity-quantum electrodynamic settings where they can be used for a variety of quantum information processing tasks.