Linear Cluster State Research Articles

QUANTUM SECURE DIRECT COMMUNICATION WITH QUANTUM IDENTIFICATION

A one-way quantum secure direct communication protocol with quantum identification utilizing two-photon three-qubit linear cluster states is proposed. The protocol can be used to transmit a secret message and identify user's identification simultaneously. The transmission of information is instantaneous, i.e. the information can be decoded during the transmission and no final transmission of additional information is needed. We prove its robustness against attacks: Any attempt of an adversary to obtain information (and even a bit of information) necessarily induces some errors that the legitimate parties could notice, even in noisy environments. Moreover, this protocol achieves a high efficiency and source capacity since more qubits can be encoded on the same photon.

Demonstration of Unconditional One-Way Quantum Computations for Continuous Variables

One-way quantum computation is a very promising candidate to fulfill the capabilities of quantum information processing. Here we demonstrate an important set of unitary operations for continuous variables using a linear cluster state of four entangled optical modes. These operations are performed in a fully measurement-controlled and completely unconditional fashion. We implement three different levels of squeezing operations and a Fourier transformation, all of which are accessible by selecting the correct quadrature measurement angles of the homodyne detections. Though not sufficient, these linear transformations are necessary for universal quantum computation.

Genuine (k, m)-Threshold Controlled Teleportation and Multipartite Entanglement

We propose genuine (k, m)-threshold controlling schemes for controlled teleportation via multi-particle entangled states, where the teleportation of a quantum state from a sender (Alice) to a receiver (Bob) is under the control of m supervisors such that k (k ≤ m) or more of these supervisors can help Bob recover the transferred state. By construction, anyone of our quantum channels is a genuine multipartite entangled state of which any two parts are inseparable. Their properties are compared and contrasted with those of the well-known GHZ, W, and linear cluster states, and also several other genuine multipartite entangled states recently introduced in the literature.

Scheme for implementing perfect quantum teleportation with four-qubit entangled states in cavity quantum electrodynamics

Recently, Peng et al. [2010 Eur. Phys. J. D 58 403] proposed to teleport an arbitrary two-qubit state with a family of four-qubit entangled states, which simultaneously include the tensor product of two Bell states, linear cluster state and Dicke-class state. This paper proposes to implement their scheme in cavity quantum electrodynamics and then presents a new family of four-qubit entangled state |Ω4〉1234. It simultaneously includes all the well-known four-qubit entangled states which can be used to teleport an arbitrary two-qubit state. The distinct advantage of the scheme is that it only needs a single setup to prepare the whole family of four-qubit entangled states, which will be very convenient for experimental realization. After discussing the experimental condition in detail, we show the scheme may be feasible based on present technology in cavity quantum electrodynamics.

Photonic multiqubit states from a single atom

We propose a protocol for the creation of photonic Greenberger-Horne-Zeilinger and linear cluster states emitted from a single atom---or ion---coupled to an optical cavity field. The method is based on laser pulses with different polarizations and exploits the atomic transition amplitudes to state-selectively achieve the desired transitions. The scheme lies within reach of current technology.

2N qubit “mirror states” for optimal quantum communication

We introduce a new genuinely 2N qubit state, known as the “mirror state” with interesting entanglement properties. The well known Bell and the cluster states form a special case of these “mirror states”, for N = 1 and N = 2 respectively. It can be experimentally realized using SWAP and multiply controlled phase shift operations. After establishing the general conditions for a state to be useful for various communicational protocols involving quantum and classical information, it is shown that the present state can optimally implement algorithms for the quantum teleportation of an arbitrary N qubit state and achieve quantum information splitting in all possible ways. With regard to superdense coding, one can send 2N classical bits by sending only N qubits and consuming N ebits of entanglement. Explicit comparison of the mirror state with the rearranged N Bell pairs and the linear cluster states is considered for these quantum protocols. We also show that mirror states are more robust than the rearranged Bell pairs with respect to a certain class of collisional decoherence.

Bound entanglement in tree graphs

In this paper, we discuss the entanglement properties of graph-diagonal states, with particular emphasis on calculating the threshold for the transition between the presence and absence of entanglement (i.e. the separability point). Special consideration is made of the thermal states of trees, including the linear cluster state. We characterize the type of entanglement present, and describe the optimal entanglement witnesses and their implementation on a quantum computer, up to an additive approximation. In the case of general graphs, we invoke a relation with the partition function of the classical Ising model, thereby intimating a connection to computational complexity theoretic tasks. Finally, we show that the entanglement is robust to some classes of local perturbations.

Splitting of quantum information using N-qubit linear cluster states

We provide a number of schemes for the splitting up of quantum information among k parties using a N-qubit linear cluster state as a quantum channel, such that the original information can be reconstructed only if all the parties cooperate. Explicit circuits are provided for these schemes, which are based on the concept of measurement based locking and unlocking of quantum information. These are experimentally feasible as they require measurements to be performed only on product basis.

Demonstration of cluster-state shaping and quantum erasure for continuous variables

We demonstrate experimentally how to remove an arbitrary node from a continuous-variable cluster state and how to shorten any quantum wires of such a state. These two basic operations, performed in an unconditional fashion, are a manifestation of quantum erasure and can be employed to obtain various graph states from an initial cluster state. Starting with a sufficiently large cluster, the resulting graph states can then be used for universal quantum information processing. In the experiment, all variations of this cluster-shaping are demonstrated on a four-mode linear cluster state through homodyne measurements and feedforward.

Six-qubit two-photon hyperentangled cluster states: Characterization and application to quantum computation

Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, i.e. polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar entanglement properties of the linear cluster state $\LCtilde$ related to the three degrees of freedom. This state has been adopted to realize various kinds of Controlled NOT (CNOT) gates, obtaining in all the cases high values of the gate fidelity. Our results demonstrate that a number of qubits $\leq$10 in cluster states of two photons entangled in multiple degrees of freedom is achievable. Furthermore, these states represent a promising approach towards scalable quantum computation in a medium term time scale. The future perspectives of a hybrid approach to one-way quantum computing based on multi-degree of freedom and multi-photon cluster states are also discussed in the conclusions of this paper.

Demonstration of a programmable source of two-photon multiqubit entangled states

We suggest and demonstrate a novel source of two-photon multipartite entangled states which exploits the transverse spatial structure of spontaneous parametric down-conversion together with a programmable spatial light modulator (SLM). The one-dimensional SLM is used to perform polarization entanglement purification and to realize arbitrary phase gates between polarization and momentum degrees of freedom of photons. We experimentally demonstrate our scheme by generating two-photon three-qubit linear cluster states with high fidelity using a diode laser pump with a limited coherence time and power on the crystal as low as $~2.5$ mW.

Universal linear Bogoliubov transformations through one-way quantum computation

We show explicitly how to realize an arbitrary linear unitary Bogoliubov (LUBO) transformation on a multimode quantum state through homodyne-based one-way quantum computation. Any LUBO transformation can be approximated by means of a fixed, finite-sized, sufficiently squeezed Gaussian cluster state that allows for the implementation of beam splitters (in form of three-mode connection gates) and general one-mode LUBO transformations. In particular, we demonstrate that a linear four-mode cluster state is a sufficient resource for an arbitrary one-mode LUBO transformation. Arbitrary-input quantum states including non-Gaussian states could be efficiently attached to the cluster through quantum teleportation.

An Optical Scheme for the Generation and Analysis of a Two Photon Six-Qubit Linear Cluster State

We present the project of an optical scheme that allows to engineer a 2-photon 6-qubit linear cluster state. By this scheme we are able to create a hyperentangled state based on polarization, linear momentum and arrival time entanglement. Since the three degrees of freedom of the photons are fully independent, the hyperentangled state allows the maximum entanglement of the particles. By suitable local unitary operations the hyperentangled state can be easily transformed into a linear cluster state, with important applications in photonic quantum computation and quantum nonlocality tests.

Atomic Cluster and Graph States: An Engineering Proposal

We suggest a simple method to generate cluster states of two-level atoms. The protocol utilizes minimum cavity/atomic resources and is based upon standard cavity QED tools alongwith Ramsey technique. Two identical atoms, each initially prepared in coherent superposition, interact simultaneously with an initially vacuum state cavity for a specified time. One atom has resonant interactions while at the same time the other one interacts dispersively. When, after completion of the interaction, cavity is again left into vacuum then atoms are shown to be entangled in bipartite cluster state. The method is also generalized to generate multi-partite linear cluster states as well as the atomic graph states.

Experimental Entanglement and Nonlocality of a Two-Photon Six-Qubit Cluster State

We create a six-qubit linear cluster state by transforming a two-photon hyperentangled state in which three qubits are encoded in each particle, one in the polarization and two in the linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, persistency of entanglement against the loss of qubits, and higher violation than in previous experiments on Bell inequalities of the Mermin type.

Error-correcting one-way quantum computation with global entangling gates

We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit cluster state that is the fundamental resource for encoded quantum teleportation is then described by a graph state containing ten vertices with constant degree seven. Universal 1WQC that incorporates error correction requires only multiple copies of this logical two-qubit state and a logical four-qubit linear cluster state, which are prepared only just in advance of their use in order to minimize the accumulation of errors. We suggest how to implement this approach in systems characterized by qubits in regular two-dimensional lattices for which entangling gates are generically global operations, such as atoms in optical lattices, quantum dots, or superconducting qubits.

Two-dimensional cluster-state preparation with linear ion traps

We present schemes to prepare two-dimensional cluster states [H. J. Briegel and R. Raussendorf, Phys. Rev. Lett. 86, 910 (2001)] with atomic ions confined in a microstructured linear ion trap and coupled by an engineered spin-spin interaction. In particular, we show how to prepare a $n\ifmmode\times\else\texttimes\fi{}2$ cluster state by creating a linear cluster state and adding third-neighbor entanglement using selective recoupling techniques. The scheme is based on the capabilities provided by segmented linear Paul traps to confine ions in local potential wells and to separate and transport ions between these wells. Furthermore, we consider creating three- and four-qubit cluster states by engineering the coupling matrix such that through the periodicity of the time evolution unwanted couplings are canceled. All entangling operations are achieved by switching of voltages and currents and do not require interaction with laser light.

Quantum logical gates with linear quadripartite cluster states of continuous variables

The concrete schemes to realize three types of basic quantum logical gates using linear quadripartite cluster states of optical continuous variables are proposed. The influences of noises and finite squeezing on the computation precision are analyzed in terms of the fidelity of propagated quantum information through the continuous variable cluster states. The proposed schemes provide direct references for the design of experimental systems implementing quantum computation with the cluster entanglement of amplitude and phase quadratures of light.

Generation of pure continuous-variable entangled cluster states of four separate atomic ensembles in a ring cavity

A practical scheme is proposed for the creation of continuous-variable entangled cluster states of four distinct atomic ensembles located inside a high-finesse ring cavity. The scheme does not require a set of external input squeezed fields, a network of beam splitters, and measurements. It is based on nothing else than the dispersive interaction between the atomic ensembles and the cavity mode and a sequential application of laser pulses of a suitably adjusted amplitudes and phases. We show that the sequential laser pulses drive the atomic ``field modes'' into pure squeezed vacuum states. The state is then examined against the requirement to belong to the class of cluster states. We illustrate the method on three examples of the entangled cluster states: the so-called continuous-variable linear, square, and T-type cluster states.

Method for generating a new class of multipartite entangled state in cavity quantum electrodynamics

Recently, Yeo and Chua introduced a genuine four-qubit entangled state |χ〉 which can implement perfect teleportation of an arbitrary two-qubit state [Y. Yeo, W.K. Chua, Phys. Rev. Lett. 96 (2006) 060502]. It has been shown that the state |χ〉 is inequivalent to the well-known Greenberger–Horne–Zeilinger state, W state, and linear cluster state, in terms of stochastic local operations and classical communication [C.F. Wu, Y. Yeo, L.C. Kwek, C.H. Oh, Phys. Rev. A 75 (2007) 032332]. This “new” class of state has many interesting entanglement properties and possible applications in quantum-information processing and fundamental tests of quantum mechanics. Here, we propose a simple scheme to generate the state |χ〉 in cavity quantum electrodynamics. Our idea may be helpful for in-depth study on such a class of state and its practical applications.