  The voltage probe model is a model of incoherent scattering in quantum
transport. Here we use this model to study the effect of spin-flip scattering
on electrical conduction through a quantum dot with chaotic dynamics. The spin
decay rate gamma is quantified by the correlation of spin-up and spin-down
current fluctuations (spin-flip noise). The resulting decoherence reduces the
ability of the quantum dot to produce spin-entangled electron-hole pairs. For
gamma greater than a critical value gamma_c, the entanglement production rate
vanishes identically. The statistical distribution P(gamma_c) of the critical
decay rate in an ensemble of chaotic quantum dots is calculated using the
methods of random-matrix theory. For small gamma_c this distribution is
proportional to gamma_c^(-1+beta/2), depending on the presence (beta=1) or
absence (beta=2) of time-reversal symmetry. To make contact with experimental
observables, we derive a one-to-one relationship between the entanglement
production rate and the spin-resolved shot noise, under the assumption that the
density matrix is isotropic in the spin degrees of freedom. Unlike the Bell
inequality, this relationship holds for both pure and mixed states. In the
tunneling regime, the electron-hole pairs are entangled if and only if the
correlator of parallel spin currents is at least twice larger than the
correlator of antiparallel spin currents.
