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Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is oneof the key signatures of quantum light and is tied to sub-Poissonian photonnumber statistics. Recently, it has been reported that photon anti-bunching orconditional sub-Poissonian photon number statistics can be obtained viasecond-order interference of mutually incoherent weak lasers and heraldingbased on photon counting. Here, we report theoretical analysis on the limits ofmanipulating conditional photon statistics via interference of weak lasers. Itis shown that conditional photon number statistics can become super-Poissonianin such a scheme. We, however, demonstrate explicitly that it cannot becomesub-Poissonian, i.e., photon anti-bunching cannot be obtained in such a scheme.We point out that incorrect results can be obtained if one does not properlyaccount for seemingly negligible higher-order photon number expansions of thecoherent state.

Limits on manipulating conditional photon statistics via interference of weak lasers