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February 8, 2001 Presented at the 3rd Workshop on Mysteries, Puzzles and Paradoxes in Quantum Mechanics, Gargnano, Italy, September 17 -23 , 2000. We show that it is possible to associate a de Broglie wavelength to a composite system even when the constituent particles are separated spatially. The nonlocal de Broglie wavelength (A/2) of a two-photon system separated spatially is measured with an appropriate detection system. The two-photon system is prepared in an entangled state in space-momentum variables. - Pacs: 42.50.-p, 42.50.Ar Key words: Quantum

References [1] M. Kacprowicz, R. Demkowicz-Dobrzanski, W. Wasilewski, K. Banaszek, and I. A. Walmsley, “Experimental quantum-enhanced estimation of a lossy phase shift”, Nature Phot. 4 , 357 (2010). [2] J. Abadie, et al. (the LIGO Scientific Collaboration), A gravitational wave observatory operating beyond the quantum shot-noise limit , Nat. Phys. 7 , 962 (2011). [3] R. Demkowicz-Dobrzanski, K. Banaszek, and R. Schnabel, “Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational wave detector GEO 600”, Phys. Rev. A 88 , 041802(R

decoherence in the QIOPA is discussed in [8 , 9]. [10] S. Popescu, in: Introduction to Quantum Computation and Information, World Scientific, New York 1998. perspective in the fundamental endeavour on quantum nonlocality [16]. Acknowledgement We acknowledge enlightening discussions and col­ laboration with S. Branca, V. Mussi, F. Bovino, and M. Lucamarini. We thank M.U.R.S.T. and the FET European Network IST-2000-29681 (ATESIT) on “Quantum Information” for funding. [11] G. Di Giuseppe, F. De Martini, D. Boschi, and S. Branca, in: Quantum Interferometry, F. De Martini