Cluster states prepared by using hot trapped ions

We propose a scheme for the preparation of one-dimensional and two-dimensional cluster states by using hot trapped ions. The scheme is based on the interaction between two ions and bichromatic radiation. The vibrational mode in our protocol is only virtually excited so that the system is insensitive to the thermal field. In addition, we only use two levels of ions as qubits and the successful probability may achieve 100%.     

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.     

Blind Quantum Signature with Controlled Four-Particle Cluster States

A novel blind quantum signature scheme based on cluster states is introduced. Cluster states are a type of multi-qubit entangled states and it is more immune to decoherence than other entangled states. The controlled four-particle cluster states are created by acting controlled-Z gate on particles of four-particle cluster states. The presented scheme utilizes the above entangled states and simplifies the measurement basis to generate and verify the signature. Security analysis demonstrates that the scheme is unconditional secure. It can be employed to E-commerce systems in quantum scenario.     

Preparation of cluster states with trapped electrons on a liquid helium surface

We present a scheme for the preparation of one-dimensional (1D) and two-dimensional (2D) cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions (the x direction) serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.     

A Scheme for Generating Cluster States via Raman Interaction

A scheme for generating cluster states via Raman interaction is proposed. In the scheme, we firstly prepare cluster states of multi-cavities with information encoded in the coherent states and then generate cluster states of multiatoms, which encode the information in the ground states of A-type atoms. The advantages of our scheme are that the atomic spontaneous radiation can be efficiently reduced since the cavity frequency is largely detuned from the atomic transition frequency and the Hadamard gate operation of the coherent states is replaced by measuring the coherent states.     

Efficient generation of two-dimensional cluster states in a cavity QED

We propose a scheme to achieve a kind of nontrivial multipartite pair-wise controlled phase operation in a cavity QED setup. The operation implemented is of geometrical nature and is not sensitive to the thermal state of the cavity. In particular, we have managed to avoid the conventional dispersive coupling so that high speed gate operation is achieved which is very important in view of decoherence. We show that this multipartite pair-wise controlled phase operation makes the generation of two-dimensional cluster states very efficient.     

Generation of Cluster States in Cavity QED

We propose two schemes for the generation of cluster states in the context of cavity quantum electrodynamics （QED）. In the first scheme, we prepare multi-cavity cluster states with information encoded in the coherent states. The second scheme is to generate multi-atom cluster states, where qubits axe represented by the states of cascade Rydberg atoms. Both the schemes axe based on the atom-cavity interaction and the atomic spontaneous radiation can be efficiently reduced since the cavity frequency is largely detuned from the atomic transition frequency.     

Teleportation of arbitrary unknown two-atom statewith cluster state via thermal cavity

This paper proposes a scheme for implementing the teleportation of an arbitrary unknown two-atom state by using a cluster state of four identical 2-level atoms as quantum channel in a thermal cavity. The two distinct advantages of the present scheme are： （i） The discrimination of 16 orthonormal cluster states in the standard teleportation protocol is transformed into the discrimination of single-atom states. Consequently, the discrimination difficulty of states is degraded. （ii） The scheme is insensitive to the cavity field state and the cavity decay for the thermal cavity is only virtually excited when atoms interact with it. Thus, the scheme is more feasible.     

Fast generation of cluster states in a linear ion trap

We propose a practical scheme to generate cluster states by simultaneously accomplishing two-qubit conditional gating on an array of equidistant ions by using transverse modes. Our operation is robust to heating and insensitive to Lamb--Dicke parameter. Meanwhile, as it is carried out in a geometric quantum computing fashion, our scheme enables the fast and high-fidelity generation of cluster states. The experimental feasibility is discussed with sophisticated ion trap techniques.     

制备囚禁离子的簇态

提出一个方案用于制备囚禁离子的簇态,制备过程中振动模仅仅是被虚激发。方案用双能级离子制备簇态,只要一束激光照射两个相互作用的离子。方案简单易行,成功几率可达到100.     

Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics （QED）, in which an unorthodox encoding is employed with the ground state being qubit [0〉 while two closely spaced upper states being qubit ｜1〉. Throughout the scheme the cavities can be in thermal states but axe only virtually excited. We show how to create the cluster states by performing a two-step hut no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.     

Cluster-state preparation in thermal cavities without single-qubit operation

A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics (QED), in which an unorthodox encoding is employed with the ground state being qubit $\left\vert 0\right\rangle $ while two closely spaced upper states being qubit $\left\vert 1\right\rangle $. Throughout the scheme the cavities can be in thermal states but are only virtually excited. We show how to create the cluster states by performing a two-step but no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.     

Generation of Ising interaction and cluster states in a one-dimensional coupled resonator waveguide

We propose a scheme for realizing the Ising spin-spin interaction and atomic cluster states utilizing the trapped two-level atoms inside a one-dimensional coupled resonator waveguide. In the strong driving and large detuning conditions, an effective Ising spin-spin interaction can be generated through suitably tuning the parameters. Then atomic cluster states are produced by using this Ising interaction. This scheme need not initially prepare the superposition states of atoms, and is insensitive to cavity decay.     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

Schemes for preparing atomic qubit cluster states in cavity QED

Two schemes are proposed for generating atomic qubits cluster states in cavity quantum electrodynamics (QED). In the first scheme, only two-atom-cavity interactions are involved, and cluster states can be directly generated by using constructed two-qubit controlled phase gates. The second scheme needs the assistance of additional single-qubit rotations, but takes less time than the first one for two-atom operations in the cavity. In this scheme, two projective operators are constructed to prepare two-dimension or more complicated configurations of cluster states. Both schemes are insensitive to the cavity decay due to the fact that the cavity is only virtually excited during the interaction between atoms and the cavity. The idea can also be applied to the ion trap system.     

Possible Realization of Cluster States and Quantum Information Transfer in Cavity QED via Raman Transition

We present a scheme to generate cluster states with many scheme, no transfer of quantum information between the atoms in cavity QED via Raman transition. In this atoms and cavities is required, the cavity fields are only virtually excited and thus the cavity decay is suppressed during the generation of cluster states. The atoms are always populated in the two ground states. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay. We also show how to transfer quantum information from one atom to another.     

Probabilistic Hierarchical Quantum Information Splitting of Arbitrary Multi-Qubit States

By utilizing the non-maximally entangled four-qubit cluster states as the quantum channel, we first propose a hierarchical quantum information splitting scheme of arbitrary three-qubit states among three agents with a certain probability. Then we generalize the scheme to arbitrary multi-qubit states. Hierarchy is reflected on the different abilities of agents to restore the target state. The high-grade agent only needs the help of one low-grade agent, while the low-grade agent requires all the other agents’ assistance. The designated receiver performs positive operator-valued measurement (POVM) which is elaborately constructed with the aid of Hadamard matrix. It is worth mentioning that a general expression of recovery operation is derived to disclose the relationship with measurement outcomes. Moreover, the scheme is extended to multiple agents by means of the symmetry of cluster states.     

Preparation of multi-atom cluster state and teleportation of arbitrary two-atom state via thermal cavity

We propose one cavity QED (CQED) scheme for generating an arbitrary 2-level-atom cluster state. Besides, by using a 4-atom cluster state as quantum channel, we propose another CQED scheme for teleporting any unknown two-atom state. In both schemes, the dynamics processes are essentially quite similar. The Rabi frequency of the classical driving field is much bigger than the detuning between the atoms and the cavity. Hence both schemes are insensitive to the cavity decay. The necessary time for implementation is much shorter than the Rydberg-atom lifespan, therefore atom decays do not need to be considered. Moreover, in the teleportation scheme the discrimination of the 16 mutually orthogonal 4-atom cluster states is transformed into the discrimination of single-atom product states, consequently the discrimination difficulty is degraded and the scheme is more easily implemented.     

Generation of four-atom cluster states in thermal cavity and implementing remote controlled not gate

We propose an experimentally feasible scheme for preparing a four-atom cluster state in a thermal cavity. In the scheme, the cavity field is only virtually excited and the photon-number-dependent part in the effective Hamiltonian is cancelled so that the system is insensitive to the cavity decay and the thermal field. At the same time, the scheme can be generalized to prepare n-atom cluster states with the success probability 100\%. In addition, using the four-atom cluster state, we also propose a simpler scheme for implementing a remote--controlled not gate (CNOT) without the Bell states measurement.     

Motional Quantum State Engineering Via a Single Laser-ion Interaction

We propose a scheme to prepare superpositions of several Fock states for the one-dimensional motion of a trapped ion. In the scheme the ion is simultaneously excited by N+1 laser beams, with the nth laser tuned to the　nth upper vibrational sideband. After a short interaction time, a measurement of the internal state may project the vibrational motion onto a superposition of the first N+1 Fock states. The scheme can be easily generalized to synthesize entangled states for the two-dimensional ion motion.