NOON state

In quantum optics, a NOON state or N00N state is a quantum-mechanical many-body entangled state:

${\displaystyle |\psi _{\text{NOON}}\rangle ={\frac {|N\rangle _{a}|0\rangle _{b}+e^{iN\theta }|{0}\rangle _{a}|{N}\rangle _{b}}{\sqrt {2}}},\,}$

which represents a superposition of N particles in mode a with zero particles in mode b, and vice versa. Usually, the particles are photons, but in principle any bosonic field can support NOON states.