  The Wigner-Araki-Yanase (WAY) theorem states that additive conservation laws
imply the commutativity of exactly implementable projective measurements and
the conserved observables of the system. Known proofs of this theorem are only
restricted to bounded or discrete-spectrum conserved observables of the system
and are not applicable to unbounded and continuous observables like a momentum
operator. In this Letter, we present the WAY theorem for possibly unbounded and
continuous conserved observables under the Yanase condition, which requires
that the probe positive operator-valued measure should commute with the
conserved observable of the probe system. As a result of this WAY theorem, we
show that exact implementations of the projective measurement of the position
under momentum conservation and of the quadrature amplitude using linear
optical instruments and photon counters are impossible. We also consider
implementations of unitary channels under conservation laws and find that the
conserved observable $L_S$ of the system commute with the implemented unitary
$U_S$ if $L_S$ is semi-bounded, while $U_S^\dagger L_S U_S$ can shift up to
possibly non-zero constant factor if the spectrum of $L_S$ is upper and lower
unbounded. We give simple examples of the latter case, where $L_S$ is a
momentum operator.
