Nonlocality of a single photon: paths to an EPR-steering experiment

Abstract

A single photon incident on a beam splitter produces an entangled field state, and in principle could be used to violate a Bell-inequality, but such an experiment (without post-selection) is beyond the reach of current experiments. Here we consider the somewhat simpler task of demonstrating EPR-steering with a single photon (also without post-selection). That is, of demonstrating that Alice's choice of measurement on her "half" of a single photon can affect the other "half" of the photon in Bob's lab, in a sense rigorously defined by us and Doherty [Phys. Rev. Lett. 98, 140402 (2007)]. Previous work by Lvovsky and co-workers [Phys. Rev. Lett. 92, 047903 (2004)] has addressed this phenomenon (which they called "remote preparation") experimentally using homodyne measurements on a single photon. Here we show that, unfortunately, their experimental parameters do not meet the bounds necessary for a rigorous demonstration of EPR-steering with a single photon. However, we also show that modest improvements in the experimental parameters, and the addition of photon counting to the arsenal of Alice's measurements, would be sufficient to allow such a demonstration.

11 pages, 6 figures. v3 changes: Correction of some minor typographical errors, some additional remarks added to the text for clarification, amendment of figure 5 and addition of figure 6

References in corpus (7)

• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox
• Entanglement, EPR-correlations, Bell-nonlocality, and Steering
• The uncertainty principle determines the non-locality of quantum mechanics
• Entanglement constrained by superselection rules
• Nonlocality of a single particle
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond

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• Optimal interferometry for Bell$-$nonclassicality by a vacuum$-$one$-$photon qubit
• Single-photon quantum nonlocality: Violation of the Clauser-Horne-Shimony-Holt inequality using feasible measurement setups
• Shareability of steering in 2-producible states
• Measuring statistics-induced entanglement entropy with a Hong-Ou-Mandel interferometer
• Single-particle entanglement gives rise to truly nonlocal effects like single-particle steering
• Hidden Steering Nonlocality in Quantum Networks
• Localization-based two-photon wave-function information encoding
• Scalable multiparty steering based on a single pair of entangled qubits