  We investigate duality in entanglement of a bipartite multi-photon system
generated from a coherent state of light. The system can exhibit polarization
entanglement if the two parts are distinguished by their parity, or parity
entanglement if the parts are distinguished by polarization. It was shown in
[PRL 110, 140404 (2013)] that this phenomenon can be exploited as a method to
test indistinguishability of two particles and it was conjectured that one can
also test indistinguishability of macroscopic systems. We propose a setup to
test this conjecture. Contrary to the previous studies using two-particle
interference effect as in Hong-Ou- Mandel setup, our setup neither assumes that
the tested state is composed of single particles nor requires that the total
number of particles be fixed. Consequently the notion of entanglement duality
is shown to be compatible with a broader class of physical systems. Moreover,
by observing duality in entanglement in the above system one can confirm that
macroscopic systems exhibit quantum behaviour. As a practical side,
entanglement duality is a useful concept that enables adaptive conversion of
entanglement of one degree of freedom (DOF) to that of another DOF according to
varying quantum protocols.
