Estimating the privacy of quantum-random numbers

We analyze the information an attacker can obtain on the numbers generated by a user by measurements on a subsystem of a system consisting of two entangled two-level systems. The attacker and the user make measurements on their respective subsystems, only. Already the knowledge of the density matrix of the subsystem of the user completely determines the upper bound on the information accessible to the attacker. We compare and contrast this information to the appropriate bounds provided by quantum state discrimination.