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AIP conference proceedings

Two-photon multiqubit hyperentangled∕cluster states

Giuseppe Vallone, R. Ceccarelli, A. Rossi, F. De Martini, Paolo Mataloni, Alexander I. Lvovsky

Published Jan 1, 2009• 0 citations
Publisher

Abstract

We describe the realization of a 6‐qubit hyperentangled state by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2‐crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. A similar scheme involving a single crystal is also discussed.

DOI
10.1063/1.3131293

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We describe the realization of a 6‐qubit hyperentangled state by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2‐crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. A similar scheme involving a single crystal is also discussed.
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 discuss two possible ways to increase the dimension of a 4-qubit hyperentangled state of two photons generated through the spontaneous parametric down conversion (SPDC) process. The two techniques are respectively based on the continuum of k-modes generated by a type I phase matched crystal and on the adoption of the time-energy entanglement as a further degree of freedom of the photons. The realization of an entangled state of two photons encoded in six (or even more) qubits, which can be transformed in a cluster state by suitable C-Phase gates, may represent a significant step towards the realization of efficient quantum computation based on the one-way model.
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric down-conversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode, and time energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2 x 2 x 3 x 3 system (36-dimensional Hilbert space), which we believe is the first reported photonic entangled system of this size to be so characterized.
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.
Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.
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.