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arXiv:quant-ph/0408047 · Physical Review A

Witnessing entanglement with second-order interference

Magdalena Stobińska, Krzysztof Wódkiewicz

Published Mar 8, 2005• 29 citations
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Abstract

Second-order interference and Hanbury-Brown and Twiss--type experiments can provide an operational framework for the construction of witness operators that can test classical and nonclassical properties of a Gaussian squeezed state, and provide entanglement witness operators to study the separability properties of correlated Gaussian squeezed sates.

DOI
10.1103/physreva.71.032304

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Second-order interference and Hanbury-Brown and Twiss--type experiments can provide an operational framework for the construction of witness operators that can test classical and nonclassical properties of a Gaussian squeezed state, and provide entanglement witness operators to study the separability properties of correlated Gaussian squeezed sates.
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The experimental study of second-order interference with fermions is much more difficult than that with bosons. Inspired by the conclusion that the behavior of two identical classical particles has exactly half fermionic and half bosonic characteristics [Phys. Rev. A88, 012130 (2013)PLRAAN1050-294710.1103/PhysRevA.88.012130], we have studied the second-order interference of fermions via the second-order interference of photons in Hanbury Brown–Twiss and Hong–Ou–Mandel interferometers, respectively. The experimental results are consistent with the theoretical predictions, which may serve as guidance for future interference experiments with fermions. The employed method offers an interesting and convenient way to study the coherence of fermions.
I briefly review second order or two-photon correlations starting from the Hanbury Brown-Twiss correlations to its modern versions in quantum optics studies. With this background, I address some foundational issues in the physics of quantum correlations and quantum entanglement and argue in favour of the validity of Einstein locality, to settle a long-standing debate. Understanding entanglement from this perspective has applications in quantum information theory, especially in gaining intuition about the relation between different measures of entanglement and its time evolution. Some examples are highlighted. I discuss how ideas on photon correlations applied to squeezing fluctuations in coherent light have become important in metrology, and perhaps crucial, in the successful operation of high sensitivity gravitational wave detectors.
We use quantum entanglement witnesses derived from Gaussian operators to study the separable criteria of continuous variable states. We transform the validity of a Gaussian witness to a Bosonic Gaussian channel problem. It follows that the maximal means of two-mode and some four-mode Gaussian operators over product pure states are achieved by vacuum (or coherent states and squeezed states) according to the properties of Bosonic Gaussian channels. Then we have necessary and sufficient criteria of separability not only for Gaussian quantum states, but also for non-Gaussian states prepared by photon adding to or/and subtracting from Gaussian states. The criterion can be further explicitly expressed with covariance matrix of the Gaussian state or covariance matrix of Gaussian kernel of the non-Gaussian state. This opens a way for precise detection of non-Gaussian entanglement.