Entanglement production in nonideal cavities and optimal opacity

Abstract

We compute analytically the distributions of concurrence $\text{C}$ and squared norm $\text{N}$ for the production of electronic entanglement in a chaotic quantum dot. The dot is connected to the external world via one ideal and one partially transparent lead, characterized by the opacity $\ensuremath{\gamma}$. The average concurrence increases with $\ensuremath{\gamma}$ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm ${\text{N}}_{0}$ is required, the average concurrence is maximal for an optimal value of the opacity ${\ensuremath{\gamma}}^{\ensuremath{\star}}({\text{N}}_{0})$ which is explicitly computed as a function of ${\text{N}}_{0}$. If ${\text{N}}_{0}$ is larger than the critical value ${\text{N}}_{0}^{\ensuremath{\star}}\ensuremath{\simeq}0.3693\ensuremath{\cdots}$, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.