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arXiv:1006.4325 · Physical Review A

Entanglement criteria for microscopic-macroscopic systems

Nicolò Spagnolo, Chiara Vitelli, Fabio Sciarrino, F. De Martini

Published Nov 1, 2010• 23 citations
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Abstract

We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [De Martini, Sciarrino, and Vitelli, Phys. Rev. Lett. 100, 253601 (2008)]. The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses that occur on the macrostate under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of separable states that can reproduce the obtained experimental results. Finally, we discuss the feasibility of a micro-macro ``genuine'' entanglement test on the analyzed system by considering different strategies, which show that in principle a fraction $\ensuremath{\varepsilon}$, proportional to the number of photons that survive the lossy process, of the original entanglement persists in any loss regime.

DOI
10.1103/physreva.82.052101

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We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [De Martini, Sciarrino, and Vitelli, Phys. Rev. Lett. 100, 253601 (2008)]. The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses that occur on the macrostate under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of separable states that can reproduce the obtained experimental results. Finally, we discuss the feasibility of a micro-macro ``genuine'' entanglement test on the analyzed system by considering different strategies, which show that in principle a fraction \ensuremathε\ensuremath{\varepsilon}\ensuremathε, proportional to the number of photons that survive the lossy process, of the original entanglement persists in any loss regime.
We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [F. De Martini et. al, Phys. Rev. Lett. 100, 253601 (2008)]. The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion allows to infer the presence of entanglement before losses, that occur on the macrostate, under specific assumptions. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of separable states that can reproduce the obtained experimental results. Finally, we discuss the feasibility of a micro-macro “genuine” entanglement test on the analyzed system by considering different strategies, which show that in principle a fraction , proportional to the number of photons that survive the lossy process, of the original entanglement persists in any losses regime. PACS numbers: 03.67.Mn, 03.65.Ud, 03.67.Bg
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define and, if not sufficiently accurate, they provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro-macro state. However, by adopting such a technique, one can surprisingly observe a violation of the CHSH inequality. This is due to the fact that ignoring the detection loophole, opened by the postselection and the system losses, can lead to misinterpretations, such as claiming the micro-macro entanglement in a setup where evidently there is not. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, so micro-micro entanglement, as it is further confirmed by the violation of a non-separability criterion for bipartite systems. How to detect photonic micro-macro entanglement in the presence of losses with currently available technology remains an open question.
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define, and if they are not sufficiently accurate they can provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully separable micro–macro state. However, by adopting such a technique one can surprisingly observe a violation of the Clauser–Horne–Shimony–Holt inequality. This is due to the fact that ignoring the detection loophole opened by the postselection and the system losses can lead to misinterpretations, such as claiming micro–macro entanglement in a setup where evidently it is not present. By using threshold detectors and postselection, one can only infer the entanglement of the initial pair of photons, and so micro–micro entanglement, as is further confirmed by the violation of a nonseparability criterion for bipartite systems. How to detect photonic micro–macro entanglement in the presence of losses with the currently available technology remains an open question.
We investigate the quantum features, entanglement and resilience to losses, of multiphoton fields generated by optical amplification of photon entangled states. We first report the realization of a class of Microscopic‐Macroscopic entangled states of more than 5×104 photons, based on parametric amplification of single‐photon and two‐photons states. A non‐locality CHSH‐type test has been performed on this system. Then, we apply a decoherence model to this Micro‐Macroscopic entangled state, showing their high resilience to photon‐loss. The theoretical results are in full agreement with many experimental observations.