Four-photon Cluster State Research Articles

Proof-of-principle demonstration of compiled Shor's algorithm using a quantum dot single-photon source.

We report a proof-of-principle demonstration of Shor's algorithm with photons generated by an on-demand semiconductor quantum dot single-photon source for the first time. A fully compiled version of Shor's algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four-photon cluster state. Genuine multiparticle entanglement properties are confirmed to reveal the quantum character of the algorithm and circuit. The implementation realizes the Shor's algorithm with deterministic photonic qubits, which opens new applications for cluster state beyond one-way quantum computing.

Efficient multi-party quantum key agreement by cluster states

A quantum key agreement (QKA) protocol by utilizing a four-photon cluster state is proposed in this paper. The proposed QKA protocol extends the two-party QKA protocol with four-qubit cluster state (Shen et al. in Quantum Inf Process 13:2313---2324, 2014) into a multi-party case. The block transmission technique and decoy photons method are used in the presented protocol. Meanwhile, the qubit efficiency of the presented protocol is also improved by using the dense coding method. Security analysis shows that the proposed protocol is secure against both participant and outside attacks.

Entanglement Concentration for Arbitrary Four-Photon Cluster State Assisted with Single Photons

We present an entanglement concentration protocol (ECP) to concentrate arbitrary four-photon less-entangled cluster state into maximally entangled cluster state. Different from other ECPs for cluster state, we only exploit the single photon as auxiliary, which makes this protocol feasible and economic. In our ECP, the concentrated maximally entangled state can be retained for further application and the discarded state can be reused for a higher success probability. This ECP works with the help of cross-Kerr nonlinearity and conventional photon detectors. This ECP may be useful in future one-way quantum computation.

Arbitrary Four-Photon Cluster State Concentration with Cross-Kerr Nonlinearity

We describe an entanglement concentration protocol (ECP) for arbitrary four-photon less-entangled cluster state. The ECP works with the help of quantum nondemolition (QND) measurement and conventional photon detectors. In our ECP, an arbitrary less-entangled four-photon cluster state can be concentrated in two steps. Moreover, in both concentration steps, the discarded states can be reused to obtain a higher success probability. This protocol may be useful in current one-way quantum computation.

Deterministic Polarization Entanglement Purification of Cluster State in Multiple Degrees of Freedom

We propose a deterministic polarization entanglement purification protocol (EPP) towards four-photon Cluster state, resorting to linear optic technology and multiple degrees of freedom (DOF). All of the participants can jointedly distill the maximally entangled states from the mixed states after transmission through a noisy channel with success probability 100 % in principle. The proposed protocol can be employed for the purification of any other multi-partite maximally entangled states, such as the Greenberger-Horne-Zeilinger (GHZ) state and W state, which is actually an universally feasible entanglement purification scheme towards multi-photon entanglement system.

Entanglement concentration for a non-maximally entangled four-photon cluster state

We present a scheme for locally concentrating a non-maximally entangled four-photon cluster state into a maximally-entangled four-photon cluster state. This scheme has a high success probability. The controlled-NOT (CNOT) gate is a crucial ingredient in this scheme, and we use a nearly deterministic CNOT gate, which is similar with that first introduced by Nemoto et al. (Phys. Rev. Lett., 2004, 93: 250502). This CNOT gate has a simple structure and does not need the strong nonlinearity.

Generation of hyperentangled four-photon cluster state via cross-Kerr nonlinearity

We propose a scheme for generating a hyperentangled four-photon cluster state that is simultaneously entangled in polarization modes and spatial modes. This scheme is based on linear optical elements, weak cross-Kerr nonlinearity, and homodyne detection. Therefore, it is feasible with current experimental technology.

An Efficient Scheme for Entanglement Concentration of Arbitrary Four-Photon States

The maximally entanglement will become less-entangled state because of the effects of decoherence. However, maximally entangled states are usually important for most of the quantum information processing protocols. So we propose a practical entanglement concentration protocol of an arbitrary four-photon less-entangled state assisted with single photons, which greatly reduces the difficulty of the experimental realization. In our scheme, we only employ three steps, a four-photon cluster state can be acquired with a certain probability by three affiliated photons. The protocol adopts the linear optical elements and weak cross-Kerr media, which make the scheme more simple and feasible in the experiment.

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state. As a pioneering three-step entanglement concentration scheme, our protocol only needs a single-photon resource to assist the concentration in each step, which makes this protocol more economical. With the help of the linear optical elements and weak cross-Kerr nonlinearity, one can obtain a maximally-entangled cluster state via local operations and classical communication. Moreover, the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.

Robust scheme for the preparation of polarization-photon cluster state with homodyne measurement via weak cross-Kerr nonlinearity

A scheme is proposed for generating a polarization four-photon cluster state based on weak cross-Kerr nonlinearity. Compared with the existing schemes, the distinct feature of the present scheme would be its preparation with near-perfect fidelity due to homodyne measurement on the probe mode. After the probe mode interacts successively with multiple signal-mode photons, sixteen terms about the signal modes can be divided into four groups with the help of homodyne measurement. Each group can be transformed into the cluster state through the appropriate local operations. Thus the present scheme has a high success probability. Because it is difficult to obtain deterministic single-photon sources for current experimental technology, the realistic success probability is rather low but is preponderant in contrast to the existing schemes.

Efficient preparation of a four-photon cluster state with homodyne measurement via cross-Kerr nonlinearity

A scheme is proposed for generating a multiphoton entangled cluster state among four modes. The scheme only uses Kerr medium, beam splitter and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. The photon in the signal mode is prepared in a superposition state of the vacuum state and one-photon state while the probe beam is initially set in a coherent state superposition. The strong probe mode interacts successively with multiple signal-mode photons, each causing a conditional phase rotation in the probe mode. Subsequent momentum quadrature homodyne measurement of the probe mode will project the photons in the signal mode into the desired entangled states. It is shown that under certain conditions, the four-photon cluster state can be generated with high fidelity and high success probability, and the scheme is feasible by current experimental technology.

Generating a Four-qubit Photon-Number Cluster State via Cross-Kerr Medium

A scheme is proposed for generating a photon-number entangled cluster state among four modes. The scheme only uses Kerr medium and homodyne measurement on probe coherent light fields, which can be efficiently made in quantum optical laboratories. The photon in the signal mode is prepared in a superposition state of the vacuum state and one-photon state while the probe beam is initially set in a intense coherent state superposition. It is shown that under certain conditions, the four-photon cluster state can be generated effectively with high success probability and homodyne detection required only once, and the scheme is feasible by current experimental technology.

Generation of Four-Photon Cluster State with Coherent Light via Cross-Kerr Nonlinearity

We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be efficiently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.

The entanglement of the four-photon cluster state

Measurement based quantum computation draws its power from the remarkable entanglement properties of the cluster states. This contribution analyses the entanglement and its persistency of an experimentally realized four-photon cluster state. We describe how spontaneous parametric down conversion together with linear optics quantum logic can be used for the experimental study.

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.