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arXiv:1210.5945 · Physical Review Letters

Reliable Entanglement Detection under Coarse-Grained Measurements

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

Published May 1, 2013• 44 citations
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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
10.1103/physrevlett.110.210502

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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.
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.
Coarse graining is a common imperfection of realistic quantum measurement, obstructing the direct observation of quantum features. Under highly coarse-grained measurement, we experimentally certify the continuous-variable nonclassicality of both Gaussian and non-Gaussian states. Remarkably, we find that this coarse-grained measurement outperforms the conventional fine-grained measurement for nonclassicality certification: it detects nonclassicality beyond the reach of the variance criterion, and furthermore, it exhibits stronger statistical significance than the high-order moments method. Our work demonstrates the usefulness of coarse-grained measurement by providing a reliable and efficient way of nonclassicality certification for quantum technologies.