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arXiv:0911.2365 · Physical Review A

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

Giuseppe Vallone, Gaia Donati, Raino Ceccarelli, Paolo Mataloni

Published May 4, 2010• 51 citations
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Abstract

Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, that is, polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar entanglement properties of the linear cluster state $|\mathrm{L͠C}{}_{6}\ensuremath{\rangle}$ related to the three degrees of freedom. This state has been adopted to realize various kinds of controlled not (cnot) gates, obtaining high values of the fidelity of the expected output states for all considered cases. Our results demonstrate that these states may represent a promising approach toward scalable quantum computation in a medium-term time scale. The future perspectives of a hybrid approach to one-way quantum computing based on multiple degrees of freedom and multiphoton cluster states are also discussed in the conclusion of this article.

DOI
10.1103/physreva.81.052301

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Cluster states of two photons and four qubits, built on the double entanglement of two photons in the degrees of freedom of polarization and linear momentum, have been used in the realization of a complete set of basic operations of one-way quantum computation. Basic computation algorithms, namely, the Grover's search and the Deutsch's algorithm, have been realized by using these states. Hyperentangled states of increasing size are of paramount importance for the realization of even more complex algorithms and can be extended to a lager number of degrees of freedom of the photons. Some recent results obtained with entangled states of two photons and six qubits are presented.
We describe the application of four-qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic operations of one-way quantum computation. These consist of arbitrary single-qubit rotations, either probabilistic or deterministic, and simple two-qubit gates, such as a controlled-NOT (CNOT) gate for equatorial qubits and a universal controlled-phase gate (controlled-ZZZ or CZ) gate acting on arbitrary target qubits. Other basic computation operations, such as the Grover's search and the Deutsch's algorithms, have been realized by using these states. In all the cases we obtained a high value of the operation fidelities. These results demonstrate that cluster states of two photons entangled in many degrees of freedom are good candidates for the realization of more complex quantum computation operations based on a larger number of qubits.
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.
Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes toward enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (that is, states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements, and functions to guarantee the setup stability, which motivates the development of technologies allowing the precise control of different photonic DOFs on a chip. We demonstrate the contextual use of path and polarization qubits propagating within an integrated quantum circuit. We tested the properties of four-qubit linear cluster states built on both DOFs, and we exploited them to perform the Grover's search algorithm according to the one-way quantum computation model. Our results pave the way toward the full integration on a chip of hybrid multi-qubit multiphoton states. Integrated optical chips performing operations with ‘hyperentangled photons’ have been fabricated by a team in Italy. Hyperentanglement, in which a photon is simultaneously entangled in several different degrees of freedom, is attracting interest because it offers a means to encode more than one quantum bit of information (qubit) onto the same photon, thus increasing the efficiency of quantum computation. However, for the approach to be practical, the hardware needed for hyperentanglement should ideally be an integrated chip platform. Professor Paolo Mataloni and co-workers have done just that using a chip that features high-quality optical waveguides written in a glass by a femtosecond laser. Their chip was used to engineer a four-qubit cluster state via hyperentanglement of the paths and polarizations of two photons. The researchers tested this cluster state by successfully performing Grover’s search algorithm.