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Advanced Science Letters

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

Raino Ceccarelli, Giuseppe Vallone, F. De Martini, Paolo Mataloni

Published Dec 1, 2009• 2 citations
Publisher

Abstract

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.

DOI
10.1166/asl.2009.1049

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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.
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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.
A six-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum, and the indistinguishable emission produced by a two-crystal system operating with type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a witness criterion specifically presented for hyperentangled states. The experiment represents a realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given ${2}^{3}\ifmmode\times\else\texttimes\fi{}{2}^{3}$ Hilbert space.
We present the results of some experimental tests of quantum nonlocality performed by two-photon states, entangled both in polarization and momentum, namely hyperentangled states and two-photon four-qubit linear cluster states. These states, which double the number of available qubits with respect to the standard two-photon entangled states, are engineered by a simple experimental method, which adopts linear optics and a single type I nonlinear crystal. The tests of local realism performed with these states represent a generalization of the Greenberger, Home, and Zeilinger (GHZ) theorem to the case of two entangled particles.
Quantum states of two photons simultaneously entangled in polarization and linear momentum, namely hyper-entangled or cluster states, allow to operate in a larger Hilbert space, since we can associate four qubits to two photons. We describe how these states are generated, characterized and manipulated by linear optics technique. Some recent results verifying that the ratio between the quantum and classical prediction grows with the size of the Hilbert space are also presented in this work. Finally, we show the efficient realization of a C-NOT gate by using two photon cluster states operating in the one-way model of quantum computation.