Advantage in two-way communication using non-classical states of light. (arXiv:1904.04596v2 [quant-ph] UPDATED)

The advantage of using a single-photon two-mode entangled state in two-way
communication via maximal violation of an inequality associated with the `Guess
Your 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 obtained
using any single-mode pure non-classical state embedded in a two-mode pure
entangled state, wherein the other mode is the vacuum (henceforth referred to
as a generalized NOON state), regardless of the average photon number of the
single mode state. For the special cases of the even-coherent, odd-coherent,
and squeezed vacuum NOON states, we establish that the advantage is also
maximal. We show that the usage of the even-coherent NOON states can provide an
advantage under noisy apparatuses (beam splitters and photo detectors). As an
aside, we study how some of these states fare in terms of violation of a
reference-frame independent Bell-type inequality.

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