  We investigate entanglement between collective operators of two wave-packets
of finite spectral bandwidth, in two different approximations of the Multimode
Parametric-Down Conversion (MPDC) process: the pairwise and the one-to-all
interaction patterns. For collective operators we choose the macroscopic
amplitudes of each wave-packet defined by the Fourier Transform of their
microscopic mode amplitudes. This approach intends, to respond to realistic
experimental conditions, where measurements apparatuses may not resolve single
microscopic mode amplitudes but rather the collective amplitude of the
wave-packets. To quantify the bipartite macroscopic entanglement we use the
logarithmic negativity. We relate the time dependent degree of macroscopic
entanglement with the complexity (number of modes and interaction pattern) and
the temperature of the system. Our results show that the macroscopic
entanglement increases linearly with the number of micro-modes in the case of
the one-to-all interaction, while in the pairwise interaction it is constant.
Moreover, in the one-to-all} pattern the birth time of entanglement and the
critical temperature decrease with increasing the number of micro-modes. We
draw the graphs associated with the two interaction patterns and related the
degree of collective entanglement with the connectivity and the index of each
vertex (mode) of the graph. We conclude that quantum information and
computation tasks may be achieved more efficiently by manipulating appropriated
collective operators in some macroscopic systems, then by using their
microscopic counterparts.
