Ladder proof of nonlocality without inequalities and without probabilities

The ladder proof of nonlocality without inequalities for two spin-$\frac{1}{2}$ particles proposed by Hardy [in New Developments on Fundamental Problems in Quantum Physics, edited by M. Ferrero and A. van der Merwe (Kluwer, Dordrecht, 1997)] and Hardy and co-workers [Phys. Rev. Lett. 79, 2755 (1997)] works only for nonmaximally entangled states and goes through for 50% of pairs at the most. A similar ladder proof for two spin-$1$ particles in a maximally entangled state is presented. In its simplest form, the proof goes through for 17% of pairs. An extended version works for 100% of pairs. The proof can be extended to any maximally entangled state of two spin-$s$ particles (with $s>~1)$.