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We examine how to signify and quantify the mesoscopic quantum coherence ofapproximate two-mode NOON states and spin-squeezed two-mode Bose-Einsteincondensates (BEC). We identify two criteria that verify a nonzero quantumcoherence between states with quantum number different by $n$. These criterianegate certain mixtures of quantum states, thereby signifying a generalised$n$-scopic Schrodinger cat-type paradox. The first criterion is the correlation$\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle\neq0$ (here $\hat{a}$ and$\hat{b}$ are the boson operators for each mode). The correlation manifests asinterference fringes in $n$-particle detection probabilities and is alsomeasurable via quadrature phase amplitude and spin squeezing measurements.Measurement of $\langle\hat{a}^{\dagger n}\hat{b}^{n}\rangle$ enables aquantification of the overall $n$-th order quantum coherence, thus providing anavenue for high efficiency verification of a high-fidelity photonic NOONstates. The second criterion is based on a quantification of the measurablespin-squeezing parameter $\xi_{N}$. We apply the criteria to theoretical modelsof NOON states in lossy interferometers and double-well trapped BECs. Byanalysing existing BEC experiments, we demonstrate generalised atomic "kitten"states and atomic quantum coherence with $n\gtrapprox10$ atoms.

Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates