Geometric constraints for orbital entanglement production in normal conductors

We investigate entanglement production in a generic normal conductor, connected to two single-channel left leads and two single-channel right leads. We consider the joint statistics of the number of entangled pairs produced during a given time and amount of entanglement carried by them. We find a constraint that implies that more entangled states are less likely to be detected. Namely, if C is the concurrence and N is the squared norm of the entangled state, then production occurs only if N(1+C)<1. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of C and N, both for systems with and without time-reversal symmetry.