  Quantum mechanics can emerge from classical statistics. A typical quantum
system describes an isolated subsystem of a classical statistical ensemble with
infinitely many classical states. The state of this subsystem can be
characterized by only a few probabilistic observables. Their expectation values
define a density matrix if they obey a "purity constraint". Then all the usual
laws of quantum mechanics follow, including Heisenberg's uncertainty relation,
entanglement and a violation of Bell's inequalities. No concepts beyond
classical statistics are needed for quantum physics - the differences are only
apparent and result from the particularities of those classical statistical
systems which admit a quantum mechanical description. Born's rule for quantum
mechanical probabilities follows from the probability concept for a classical
statistical ensemble. In particular, we show how the non-commuting properties
of quantum operators are associated to the use of conditional probabilities
within the classical system, and how a unitary time evolution reflects the
isolation of the subsystem. As an illustration, we discuss a classical
statistical implementation of a quantum computer.
