Concentration of higher dimensional entanglement

Enhancement of entanglement enhancement is necessary for most quantum communication protocols many of which are defined in Hilbert spaces larger than two. In this work we present the experimental realization of entanglement concentration of orbital angular momentum entangled photons produced in the spontaneous parametric down-conversion process which have been shown to provide a source for higher dimensional entanglement. We investigate the specific case of three dimensions and the possibility of generating different entangled states out of an initial state. The results presented here are of importance for pure states as well as for mixed states. PACS Numbers: 3.65 Bz, 3.67 -a, 42.50 Ar Typeset using REVTEX 1 Most of the current applications of entanglement in quantum communication such as quantum teleportation [1] and quantum cryptography [2,3] work best for maximally entangled states. However, in practice one always has to deal with non maximally entangled or mixed states for example because of the uncontrollable interaction of the particles with the environment. Therefore many quantum protocols such as distillation [4,5] purification [6], concentration [7] and error correction [8,9] have been suggested in order to enhance the quality of entanglement. With the exception of quantum error correction which is most important for quantum computation, the common idea in all other protocols is to start with a sample of entangled states having a low quality of entanglement and using local operations and classical communication only to end up in a smaller ensemble with a higher degree of entanglement. A measure for the enhancement of the entanglement could for example be the non local feature of the state represented by violation of Bell’s inequalities. There are varying terminologies in the literature. Following reference [7] we will use the term concentration for our experimental achievement which was to extract maximally entangled states out of non maximally entangled pure states. This method is also referred to as local filtering or the ”Procrustean method” . In contrast to concentration the term distillation is used for the more general case of extracting entanglement out of initially mixed states. Purification denotes the procedure which makes arbitrary initial states more pure, after local operations and classical communication, but not necessarily more entangled. As demonstrated by Horodecki et al. [4], even if the fidelity of the system to be in the desired entangled state is less than 1/2, all inseparable quantum systems can be distilled to singlet states by local filtering and the Bennett et al. distillation protocol [6]. This means that the Procrustean concentration method as experimentally demonstrated here is not only of importance for pure states but also for extracting entanglement out of mixed states. After Procrustes, a fabulous Greek giant who stretched or shortened captives to fit one of his iron beds