Experimental verification of the commutation relation for Pauli spin operators using single-photon quantum interference

We report experimental verification of the commutation relation for Pauli spin operators using the single-photon polarization state. The experimental quantum operation corresponding to the commutator, [σz,σx]=kσy[σz,σx]=kσy, showed process fidelity of 0.94 compared to the ideal σyσy operation and |k||k| is determined to be 2.12±0.182.12±0.18.