Multiparty multilevel energy-time entanglement

Franson-like setups are inadequate for multiparty Bell experiments with energy-time entanglement because postselected events can depend on the local settings, and local models can exploit this feature to reproduce the quantum predictions, even in the case of ideal devices. We extend a previously introduced interferometric scheme [A. Cabello et al., Phys. Rev. Lett. 102, 040401 (2009)] to solve this problem in the N-qubit and N-quNit cases. In addition, the proposed setups allow us to prepare and test N-qubit Greenberger-Horne-Zeilinger and (Sigma(N)(i=1) vertical bar i ... i) /root N energy-time entangled states.