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We study orbital entanglement production in a chaotic cavity connected to four single-channel normal-metal leads and one superconducting lead, assuming the presence of time-reversal symmetry and within a random matrix theory approach. The scattered state of two incident electrons is written as the superposition of several two-outgoing quasi-particle components, four of which are orbitally entangled in a left-right bipartition. We calculate numerically the mean value of the squared norm of each entangled component, as functions of the number of channels in the superconducting lead. Its behavior is explained as resulting from the proximity effect. We also study statistically the amount of entanglement carried by each pair of outgoing quasi-particles. When the influence of the superconductor is more intense, the device works as an entangler of electron-hole pairs, and the average entanglement is found to be considerably larger than that obtained without the superconducting lead.

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 $\mathcal{C}$ is the concurrence and $\mathcal{N}$ is the squared norm of the entangled state, then production occurs only if $\mathcal{N}(1+\mathcal{C})l1$. For the particular case of a chaotic cavity working as quantum entangler, we obtain explicit expressions for the joint distribution of $\mathcal{C}$ and $\mathcal{N}$, both for systems with and without time-reversal symmetry.

A stub model is introduced to describe the charge transport properties of a system consisting of an arbitrary number of noncollinear ferromagnetic or normal reservoirs coupled nonideally to a normal metal chaotic cavity. We characterize the contacts by a reduced set of parameters which can be used to express the average value of any charge-transfer cumulant. Explicit expressions of this set of parameters are given for the cases of ideal ballistic contacts and tunnel junctions. The average conductance and shot-noise power of a two terminal FNF device with noncollinear ferromagnetic reservoirs are calculated analytically via an extended diagrammatic method which allows for the importation of all diagrams of the corresponding NNN system. We observe that the Fano factor exhibits a transition between monotonic and nonmonotonic behaviors as a function of the reservoir's relative magnetization angle. A diagram of this transition in the plane of the polarization parameters is shown. With straightforward modifications, our scheme paves the way for efficient calculations of the average value of an arbitrary cumulant of the charge-transfer statistics in hybrid devices along with its quantum corrections.

We study the current-induced torque for electrons on ferromagnet-normal metal-ferromagnet (FNF) trilayer with non-collinear magnetizations. Our system is composed of a chaotic cavity and two junctions, coupled with ideal contacts to ferromagnetic reservatories in local equilibrium by means of a small number of scattering channels. We assume that the normal part is disordered. Each junction is related to the direction of the reservoirs magnetization. The system is taken out of equilibrium causing a spin accumulation. We suppose that all elements have a length smaller than the coherence phase and the spin flip lengths. This consideration lets us neglect decoherence and spin flip processes. The conductance and torque were found numerically by employing the random-matrix theory and scattering matrix formalism for the spin-flux. The observables are presented as a function of the number of propagating channels in the extreme quantum limit regime and of the angle between the magnetizations of the different ferromagnet layers.