 The quantum state of composite particles, made of elementary fermions, can exhibit a wide range of behavior, from fermionic to bisonic, depending on the experimental situation considered. This behavior is captured by fundamental operations, such as single-particle addition and subtraction, and two-particle interference. We analyze these operations for systems of a finite number of particles, and construct optimal Krause operators to implement them. We then measure the quality of bisonic and fermionic behavior in terms of single-particle addition, and subtraction, and two-particle interference. For composite particles made of two distinguishable fermions, we find a transition from fermionic to bisonic behavior as a function of entanglement between the constituents. We also apply these considerations to composite particles of two distinguishable bosons, and identify the relation between entanglement and bisonic behavior for these systems. This article was authored by Paul Kozinski, Ravishon Karamanathan, Okihito Soeda, and others. We are article.tv, links in the description below.