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

TL;DR

This paper experimentally verifies the fundamental commutation relation of Pauli spin operators using single-photon quantum interference, demonstrating the phase difference and fidelity of the quantum operations involved.

Contribution

It presents the first experimental implementation of the Pauli commutation relation using quantum interference of single-photon polarization states.

Findings

Process fidelity of 0.94 with the ideal $\sigma_y$ operation.

Measured $|k|$ value of $2.12\pm0.18$ for the commutator.

Confirmed the phase factor of $\pi$ between $\sigma_z \sigma_x$ and $\sigma_x \sigma_z$.

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 $2.12\pm0.18$.