Abstract
The Clauser–Horne–Shimony–Holt (CHSH) experiment is an essential test of nonlocality in quantum mechanics and can be used to validate the principle of entanglement. In addition to verifying entanglement, the measurable CHSH parameter can also be used to gauge the quality of the entanglement present in a system. The measurement of Hong–Ou–Mandel (HOM) interference is another important fundamental experiment in quantum optics that measures the indistinguishability of a pair of photons. In this article, we demonstrate how the results of a HOM interference experiment, a relatively simple experiment, can be used to obtain an estimate for the value of the CHSH <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S$</tex-math></inline-formula> parameter, which is a more complicated measurement. We experimentally demonstrate that the HOM interference technique is capable of providing an estimate of the value of the CHSH parameter that is within one standard deviation of measurement error when spectral impairments are present. We expect that this technique will aid in the calibration of quantum optical systems.
Highlights
Entanglement [1]–[3] is a vital resource for quantum information protocols
We demonstrate how one could use HOM interference to demonstrate the indistinguishability of the photons generated by a source, but to estimate the S parameter value that would be obtained when using these photons in a CHSH experiment
Each path consists of a polarization controllers (PC) for polarization alignment, a narrow bandpass filter (NBPF) with a 1 nm bandwidth centered around 1544 nm, and a wide bandpass filter (WBPF) to filter out residual pump light and noise photons in the near infrared unintentionally injected by the NBPF
Summary
Entanglement [1]–[3] is a vital resource for quantum information protocols. High quality entangled quantum systems are required for certain secure communication protocols [4] and quantum teleportation [5]. We demonstrate how one could use HOM interference to demonstrate the indistinguishability of the photons generated by a source, but to estimate the S parameter value that would be obtained when using these photons in a CHSH experiment. In the ideal case, where we neglect spectral effects and the SPDC source emits signal and idler photons of the same angular frequency ω0, we have f (ωs, ωi) = δ(ωs − ω0)δ(ωi − ω0) In this situation, there are no terms in the state of Eq (15) that give coincidence counts at τ = 0. Where the quantities I and K(τ ) are defined as they were in Eq (9)
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