Statistics of orbital entanglement production in quantum-chaotic dots

The production of orbitally entangled electrons in quantum-chaotic dots is investigated from a statistical point of view. The degree of entanglement is quantified through the concurrence and the entanglement of formation. We calculate the complete statistical distributions of the entanglement measures by using random matrix theory. Simple analytical expressions are provided for the concurrence distributions. We identify clear signatures of time-reversal invariance in the production of entanglement at the level of the entanglement-measure distributions, such as the ability of producing maximally entangled (Bell) states, which passed unnoticed in previous works, where only the first two moments of the distributions were studied.

Figure 1

The quantum dot orbital entangler. The left and right leads are attached to chemical potentials ${\mu }_L$ and ${\mu }_R$, respectively. As explained in the text, an electron leaving the dot to the left (right) side can escape through the leads 1 or 2 (3 or 4), defining a two-level quantum system.

Figure 2

Distribution of concurrence in the presence $(\beta =1)$ and absence $(\beta =2)$ of time-reversal invariance. Insets: Numerical verification of the $P_{\beta }\left(\mathcal{E}\right)$. A good agreement between theory and numerics can be observed in both symmetry cases.

Figure 3

Entanglement of formation distributions in the presence $(\beta =1)$ and absence of time-reversal invariance $(\beta =2)$.