Loophole-free Bell test with multi-photon-subtracted two-mode squeezed state

We investigate the loophole-free Bell inequality test with a multi-photon-subtracted two-mode squeezed state (TMSS). The maximal loophole-free Bell inequality violation is S = 2.046 for bi-side single-photon-subtracted TMSS. We show that such a violation can be further improved to S = 2.070 for ideal bi-side five-photon subtractions. Such a result approaches Munro's optimal bound for loophole-free Bell inequality violation. We further develop a concise phase-space method for deriving the loophole-free Bell inequality violation, which enables us to obtain a series of numerical results for practical multi-photon subtraction with a beam splitter and photon detectors. Our results provide a physically implementable state for approaching Munro's optimal bound.