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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Reliable Entanglement Detection Under Coarse-Grained Measurements

Stephen Patrick Walborn, Łukasz Rudnicki, D. S. Tasca, Rafael M. Gomes, Fabricio Toscano

Published Jan 1, 2013• 3 citations
Publisher

Abstract

We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a ``false positive" for identification of entanglement, under any degree of coarse graining. We show that, even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.

DOI
10.1364/cqo.2013.t5b.2

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We derive reliable entanglement witnesses for coarse-grained measurements on continuous variable systems. These witnesses never return a ``false positive" for identification of entanglement, under any degree of coarse graining. We show that, even in the case of Gaussian states, entanglement witnesses based on the Shannon entropy can outperform those based on variances. We apply our results to experimental identification of spatial entanglement of photon pairs.
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Continuous-variable systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\ensuremath{\sim}60%$ relative to 7344 studied cases.