  We reveal a close relationship between quantum metrology and the
Deutsch-Jozsa algorithm on continuous variable quantum systems. We develop a
general procedure, characterized by two parameters, that unifies parameter
estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we
keep constant, the procedure implements either the parameter estimation
protocol or the Deutsch-Jozsa algorithm. The parameter estimation part of the
procedure attains the Heisenberg limit and is therefore optimal. Due to the use
of approximate normalizable continuous variable eigenstates the Deutsch-Jozsa
algorithm is probabilistic. The procedure estimates a value of an unknown
parameter and solves the Deutsch-Jozsa problem without the use of any
entanglement.
