Cluster-class State Research Articles

Practical entanglement concentration of nonlocal polarization-spatial hyperentangled states with linear optics

We present some different hyperentanglement concentration protocols (hyper-ECPs) for nonlocal N-photon systems in partially polarization-spatial hyperentangled states with known parameters, resorting to linear optical elements only, including those for hyperentangled Greenberger---Horne---Zeilinger-class states and the ones for hyperentangled cluster-class states. Our hyper-ECPs have some interesting features. First, they require only one copy of nonlocal N-photon systems and do not resort to ancillary photons. Second, they work with linear optical elements, neither Bell-state measurement nor two-qubit entangling gates. Third, they have the maximal success probability with only a round of entanglement concentration, not repeating the concentration process some times. Fourth, they resort to some polarizing beam splitters and wave plates, not unbalanced beam splitters, which make them more convenient in experiment.

Probabilistically Controlled Teleportation of an Arbitrary Two-Qubit State via Positive Operator-Valued Measure

We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.

An entanglement concentration protocol for cluster states

Cluster class states are entangled states which have several uses in quantum information and computation problems. In this paper we develop an entanglement concentration protocol for partially entangled pure cluster class state with an even number of qubits. We use only local operations for this protocol.

Probabilistic and Controlled Teleportation of an Arbitrary Two-Qubit State via One Dimensional Five-Qubit Cluster-Class State

We propose a three-party scheme for probabilistically teleporting an arbitrary two-qubit state. In the scheme, a one-dimensional five-qubit cluster-class state is utilized as the quantum channel. The sender performs two Bell-state measurements (BSMs) on the qubits at hand and the controller makes a single-qubit measurement. With the sender’s and the controller’s helps, the receiver can reconstruct the original state with a certain probability by introducing an auxiliary qubit and making appropriate unitary operations. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.

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.

REMOTE PREPARATION OF TWO-QUBIT ENTANGLED STATE VIA ONE-DIMENSIONAL FOUR-QUBIT CLUSTER AND CLUSTER-CLASS STATES

We propose two protocols for remotely preparing a two-qubit entangled state, where the quantum channels take the form of one-dimensional four-qubit cluster and cluster-class states, respectively. The total success probability and classical communication cost are also calculated.

Three-Party Quantum Information Splitting of an Arbitrary Two-Qubit State by Using Six-Qubit Cluster State

We propose a scheme for splitting an arbitrary two-qubit state among three parties by using a six-qubit cluster-class state as a quantum channel. Based on two Bell-state measurements (BSMs) and a two-qubit projective measurement, any one of the two agents can reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information.

量子隐形传态的类簇态信道方案

A scheme for teleportation of an arbitrary two-qubit state using a four-qubit linear cluster-class state is proposed.Quantum teleportation can be successfully realized with a certain probability if the receiver can adopt an appropriate collective unitary transformation after receiving the sender's Bell-state measurement information.The scheme is more practical than previous ones using maximally entangled states as the quantum channel.In addition,an important conclusion is obtained from the above scheme that a maximally four-qubit entangled state(cluster state)is extracted from a single copy of the cluster-class state with the same probability as the teleportation.

Teleportation of an Arbitrary Two-Particle State via a Single Cluster-Class State

Teleportation of an arbitrary two-qubit state with a single partially entangled state, a four-qubit linear cluster-class state, is studied. The case is more practical than previous ones using maximally entangled states as the quantum channel. In order to realize teleportation, we first construct a cluster-basis of 16 orthonormal cluster states. We show that quantum teleportation can be successfully implemented with a certain probability if the receiver can adopt appropriate unitary transformations after receiving the sender's cluster-basis measurement information. In addition, an important conclusion can be obtained that a four-qubit maximally entangled state (cluster state) can be extracted from a single copy of the cluster-class state with the same probability as the teleportation in principle.

Three-Party Quantum State Sharing of an Arbitrary Unknown Two-Qubit State Based on Entanglement Swapping and Bell-State Measurements

We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate (QCPG) operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.

PROBABILISTIC TELEPORTATION OF AN ARBITRARY TWO-QUBIT STATE VIA ONE-DIMENSIONAL FOUR-QUBIT CLUSTER-CLASS STATE

An explicit scheme for probabilistically teleporting an arbitrary two-qubit state is proposed by using a one-dimensional four-qubit cluster-class state as the quantum channel. In the scheme, the sender first performs two Bell state measurements (BSMs). Then with the sender's help, the receiver can reconstruct the original state probabilistically by introducing an auxiliary qubit and making appropriate unitary operations. Moreover, the total success probability and classical communication cost of the present scheme are also calculated.

Permutation-invariant monotones for multipartite entanglement characterization

In this work we consider the permutational properties of multipartite entanglement monotones. Based on the fact that genuine multipartite entanglement is a property of the entire multiqubit system, we argue that ideal definitions for its characterizing quantities must be permutation invariant. Using this criterion, we examine the three four-qubit entanglement monotones introduced by Osterloh and Siewert [Phys. Rev. A 72, 012337 (2005)]. By expressing them in terms of quantities whose permutational properties can be easily derived, we find that one of these monotones is not permutation invariant. We propose a permutation-invariant entanglement monotone to replace it, and show that our new monotone properly measures the genuine four-qubit entanglement in four-qubit cluster-class states. Our results provide some useful insights in understanding multipartite entanglement.

Multipartite entanglement in four-qubit cluster-class states

Based on quantitative complementarity relations (QCRs), we analyze the multipartite correlations in four-qubit cluster-class states. It is proven analytically that the average multipartite correlation ${E}_{ms}$ is entanglement monotone. Moreover, it is also shown that the mixed three-tangle is a correlation measure compatible with the QCRs in this kind of quantum state. More arrestingly, with the aid of the QCRs, a set of hierarchy entanglement measures is obtained rigorously in the present system.