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 (5)

• On the Measurement of Qubits
• A Delayed Choice Quantum Eraser
• Reversing the Weak Quantum Measurement for a Photonic Qubit
• Experimental demonstration of bosonic commutation relation via superpositions of quantum operations on thermal light fields
• Scheme for proving the bosonic commutation relation using single-photon interference

Cited by in corpus (7)

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• Experimental demonstration of decoherence suppression via quantum measurement reversal
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• Ultra-low noise single-photon detector based on Si avalanche photodiode
• Direct experimental test of commutation relation via weak value
• Scheme for directly observing the non-commutativity of the position and the momentum operators with interference
• Teaching Quantum Mechanical Commutation Relations via an Optical Experiment