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arXiv:0906.2233 · Physical Review Letters

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

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

Published Oct 13, 2009• 120 citations
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Abstract

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.

DOI
10.1103/physrevlett.103.160401

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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.
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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.
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.
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.
Cluster states serve as the central physical resource for one-way quantum computing. We here present an experimental demonstration of the efficient cluster-state construction scheme proposed by Browne and Rudolph. In our experiment, three-photon cluster states with high purity are created from two Bell states via a qubit ``fusion'' operation, showing a strong violation of a three-particle Mermin inequality of $\ensuremath{\mid}⟨A⟩\ensuremath{\mid}=3.10\ifmmode\pm\else\textpm\fi{}0.03$. In addition, the entanglement properties of the cluster states are examined under ${\ensuremath{\sigma}}_{z}$ and ${\ensuremath{\sigma}}_{x}$ measurements on a qubit. This scheme could be extended to any desired number of qubits and represents an essential step for the optical one-way quantum computation.