Violations of Local Realism by Two EntangledN-Dimensional Systems Are Stronger than for Two Qubits

Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in $N$-dimensional Hilbert spaces, or “ $\mathrm{qu}N\mathrm{its}$.” Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled $\mathrm{qu}N\mathrm{its}$ ( $3\le N\le 9$) than for two qubits and that they increase with $N$. The two $\mathrm{qu}N\mathrm{it}$ measurements can be experimentally realized using entangled photons and unbiased multiport beam splitters.