1. Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
2. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, 1090 Wien, Austria
3. Present address: Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

Correspondence to: Anton Zeilinger^1,2 Correspondence and requests for materials should be addressed to A.Z. (Email: zeilinger-office@quantum.at).

Abstract

Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments^{1, 2, 3, 4}. Quantum entanglement⁵, the coherent superposition of states in multi-particle systems, yields more complex phenomena^{6, 7}. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging⁸; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit^{9, 10, 11, 12}, or quantum lithography beyond the classical diffraction limit¹³. It has been generally understood¹⁴ that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons^{15, 16, 17, 18}. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.

1. Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
2. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, 1090 Wien, Austria
3. Present address: Physikalisches Institut, Universität Heidelberg, D-69120 Heidelberg, Germany

Correspondence to: Anton Zeilinger^1,2 Correspondence and requests for materials should be addressed to A.Z. (Email: zeilinger-office@quantum.at).

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