Quantum entanglement in composite systems

We discuss a certain class of models of mesoscopic quantum phenomena that result from associating a particular type of Hamiltonian dynamics with the entangled states of composite systems. Using such models, we can concisely describe the phenomenology of a two-dimensional electron gas, in particular, the quantum Hall effect. We show how such models (if they are regarded as reflecting actual physical principles and not only the phenomenology) can be tested by a quantum teleportation-type experiment. The so-called mesoscopic models stipulate that the dynamics of a two-dimensional gas coupled to an ambient field is captured by a functional of the type $\operatorname{Tr}[H\rho]+\beta\operatorname{Tr} f(\rho)$, where $\rho$ is the density operator and $H$ is a single-particle Hamiltonian. We use the proposed approach to demonstrate that a suitable quantum teleportation experiment can provide information about the analytic function $f$. This leads us to view the composite system of an electron gas and an ambient field as a natural quantum computer.