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The advantage of using a single-photon two-mode entangled state in two-waycommunication via maximal violation of an inequality associated with the `GuessYour Neighbour's Input' (GYNI) game has been theoretically [Phys. Rev. Lett.120, 060503 (2018)] as well as experimentally [CLEO FID.4 (OSA, 2018)]established quite recently. We show that such an advantage can also be obtainedusing any single-mode pure non-classical state embedded in a two-mode pureentangled state, wherein the other mode is the vacuum (henceforth referred toas a generalized NOON state), regardless of the average photon number of thesingle mode state. For the special cases of the even-coherent, odd-coherent,and squeezed vacuum NOON states, we establish that the advantage is alsomaximal. We show that the usage of the even-coherent NOON states can provide anadvantage under noisy apparatuses (beam splitters and photo detectors). As anaside, we study how some of these states fare in terms of violation of areference-frame independent Bell-type inequality.

Advantage in two-way communication using non-classical states of light