Entanglement production in non-ideal cavities and optimal opacity

TL;DR

This paper analytically studies how the opacity of a quantum dot's lead affects entanglement production, revealing an optimal opacity for maximizing entanglement under detection constraints.

Contribution

It provides explicit formulas for entanglement distributions in a chaotic quantum dot with mixed lead transparency, identifying the optimal opacity for entanglement detection.

Findings

Average concurrence increases with opacity

Maximum entanglement occurs at an optimal opacity for certain detection thresholds

Entanglement production is maximized in the ideal case beyond a critical detection threshold

Abstract

We compute analytically the distributions of concurrence $\bm{\mathcal{C}}$ and squared norm $\bm{\mathcal{N}}$ 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 $\gamma$. The average concurrence increases with $\gamma$ while the average squared norm of the entangled state decreases, making it less likely to be detected. When a minimal detectable norm $\bm{\mathcal{N}}_0$ is required, the average concurrence is maximal for an optimal value of the opacity $\gamma^\star(\bm{\mathcal{N}}_0)$ which is explicitly computed as a function of $\bm{\mathcal{N}}_0$. If $\bm{\mathcal{N}}_0$ is larger than the critical value $\bm{\mathcal{N}}_0^\star\simeq 0.3693\dots$, the average entanglement production is maximal for the completely ideal case, a direct consequence of an interesting bifurcation effect.