  Secure random numbers are a fundamental element of many applications in
science, statistics, cryptography and more in general in security protocols. We
present a method that enables the generation of high-speed unpredictable random
numbers from the quadratures of an electromag- netic field without any
assumption on the input state. The method allows to eliminate the numbers that
can be predict due the presence of classical and quantum side information. In
particular, we introduce a procedure to estimate a bound on the conditional
min-entropy based on the Entropic Uncertainty Principle for position and
momentum observables of infinite dimensional quantum sys- tems. By the above
method, we experimentally demonstrated the generation of secure true random
bits at a rate greater than 1 Gbit/s.
