Fragility of a class of highly entangled states withnqubits

We consider a quantum computer with $n$ quantum bits (“qubits”), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we define a parameter indicating quantum uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with $1/\sqrt{n}$ for all those states which have been exposed to the environment. Furthermore we consider a quantum computer with perfect 1-qubit gates and two-qubit gates with a depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.