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

Abstract

We report experimental verification of the commutation relation for Pauli spin operators using quantum interference of the single-photon polarization state. By superposing the quantum operations ${\sigma }_z{\sigma }_x$ and ${\sigma }_x{\sigma }_z$ on a single-photon polarization state, we have experimentally implemented the commutator, $[{\sigma }_z,{\sigma }_x]$, and the anticommutator, $\{{\sigma }_z,{\sigma }_x\}$, and have demonstrated the relative phase factor of $\pi$ between ${\sigma }_z{\sigma }_x$ and ${\sigma }_x{\sigma }_z$ operations. The experimental quantum operation corresponding to the commutator, $[{\sigma }_z,{\sigma }_x]=k{\sigma }_y$, showed process fidelity of 0.94 compared to the ideal ${\sigma }_y$ operation and $|k|$ is determined to be $2.12\pm 0.18$.

4pages, 3 figures

References in corpus (1)

• Scheme for proving the bosonic commutation relation using single-photon interference