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International Journal of Quantum Information

GENERATING AND DISTRIBUTING TWO-PHOTON ENTANGLED SPATIAL QUDITS

G. Lima, Leonardo Neves, Ivan F. Santos, Carlos Henrique Monken, J. G. Aguirre Gómez, C. Saavedra, Sebastião Pádua

Published Feb 1, 2007• 4 citations
Publisher

Abstract

We report an experiment to generate and propagate two entangled spatial qudits, [Formula: see text]-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with [Formula: see text]-slits in the arms of the down-converted photons, we associate the qudit space with the [Formula: see text] possible paths followed by each photon. Experimental results for qudits with [Formula: see text] and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form.

DOI
10.1142/s0219749907002815

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We report an experiment to generate and propagate two entangled spatial qudits, [Formula: see text]-dimensional quantum systems, using spontaneous parametric down-conversion. The manipulation, via pump beam, of the transverse spatial correlation between the photon pairs is explored. Inserting apertures with [Formula: see text]-slits in the arms of the down-converted photons, we associate the qudit space with the [Formula: see text] possible paths followed by each photon. Experimental results for qudits with [Formula: see text] and 8 are shown. We demonstrate that the generated states cannot be classically correlated. We also show the propagation of entangled states of spatial qudits. Their free-space distribution is performed at the laboratory scale and the propagated states maintain a high fidelity with their original form.
We report an experiment to generate entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D slits in the arms of the twin photons define the qudit space. By manipulating the pump beam correctly, the twin photons will pass only by symmetrically opposite slits, generating entangled states between these different paths. Experimental results for qudits with D = 4 and 8 are shown. We demonstrate that the generated states are entangled states.
We review recent theoretical and experimental works where are proposed and demonstrated how to use photon pairs created by spontaneous parametric down-conversion to generate entangled states of D-dimensional quantum systems, or qudits. This is the first demonstration of high-dimensional entanglement based on the intrinsic transverse momentum entanglement of the type-II down-converted photons. The qudit space is defined by an aperture made up of an opaque screen with D slits (paths), placed in the arms of the twin photons. By manipulating the pump beam profile we can prepare different entangled states of these possible paths. We focus our attention on an important case for applications in quantum information: the maximally entangled states. Experimental results for qudits with D=4 and D=8 are shown and measuring a two-photon conditional interference, we also demonstrate the nonclassical character of the correlations.
We show the propagation of entangled states of high-dimensional quantum systems. The qudits states were generated using the transverse correlation of the twin photons produced by spontaneous parametric down-conversion. Their free-space distribution was performed at the laboratory scale and the propagated states maintained a high fidelity with their original form. The use of entangled qudits allow an increase in the quantity of information that can be transmitted and may also guarantee more privacy for communicating parties. Therefore, studies about propagating entangled states of qudits are important for the effort of building quantum communication networks.
In this thesis, we explore the properties of photons generated by parametric down-conversion (PDC) and entangled in continuous variables of transverse momentum, with the aim of using this degree of freedom for developing a new method for generating en-tangled states in discrete and multidimensional spaces. Such states have a great potential for applications in fundamental problems of quantum mechanics as well as in quantum information protocols. Our study is based on the theory of angular spectrum transfer from the laser beam tothe two-photon state, proposed and demonstrated by Monken, Souto Ribeiro and P Ladua [Phys. Rev. A 57, 3123 (1998)]. Using it, we investigate theoretically the evolution of the quantum state of photon pairs when they propagate from the crystal and are transmitted through linear optical systems like lenses and apertures. The two-photon state is calculated when there is only one optical system in the path of each photon and we also discuss the generalization of the method employed in the calculation, for more complex experiments. With the two-photon state obtained, we propose a method for generating entangledstates of qubits (two-dimensional quantum systems) and qudits (D-dimensional quantum systems), using the transverse momentum of photons from PDC. The method is based on the selection of specific transverse spatial modes of each photon, by using an array of D-slits (D . 2) in the path of these photons. In this method we have the control of the dimension, D, of each qudit and also the degree of entanglement between them, by manipulating the transverse laser beam profile, which is due to the transfer of angular spectrum. In order to test the theory, we make an experiment for a specific case, which has a great interest in practical applications of entanglement: we demonstrate the generation of maximally entangled states of qudits with D = 4 and D = 8. The quantum character of the correlations is assured qualitatively by measuring two-photon interference patterns with conditional fringes. We also investigate the propagation of these entangled states of qudits through free space and with a simple experiment we show that they can be distributed for distant and spatially separated parts, keeping the correlations. Finally, we perform an experiment for quantifying entanglement in this type of state that we are producing. In this work, we restrict ourselves to the simplest case of two qubits. We prepare different states by manipulating the transverse laser beam profile and their degree of entanglement is measured in two ways: (i) through the degree ofconditionality of the two-photon interference patterns and (ii) through the measurement of marginal probability. We discuss the extension of the method (i) for two-qudit states.
Higher dimensional quantum systems have a very important role to play in quantum information, computation as well as communication. In photonic systems, it is common to use the photon's polarization degree of freedom for various investigations. However, this restricts us to only two orthogonal states, hence qubits for manipulation. In this paper, we have theoretically analysed and experimentally demonstrated a system of two photonic qutrits which are correlated in the spatial degree of freedom. The qutrits have been generated by modulating the pump beam in a spontaneous parametric down conversion process using an aperture based system. In principle, this system can be scaled up to generation of even higher dimensional correlated qudits with possible application for quantum communication and computation implementations.
Discretizing transverse linear momentum of photon pairs, generated by spontaneous parametric down conversion (SPDC), is one of the simplest methods for producing bipartite entangled states in high dimensions. So far, it has been employed only to prepare states in dimensions $m\ifmmode\times\else\texttimes\fi{}m$. In this work, we study the generalization for engineering entangled states in dimensions $m\ifmmode\times\else\texttimes\fi{}n$. Our approach relies on the manipulation of the pump beam transverse profile and the phase-matching function of the SPDC process to prepare, behind an mmm- and nnn-slit aperture, different $m\ifmmode\times\else\texttimes\fi{}n$ spatial entangled states. We demonstrate the technique experimentally for some $2\ifmmode\times\else\texttimes\fi{}3$ states. Compared to previous approaches in producing $2\ifmmode\times\else\texttimes\fi{}n$ photonic entanglement, which require either more than two photons or hybrid entanglement, our scheme is less demanding and simpler since we employ only two photons and a single degree of freedom to encode the states.