  Joint or simultaneous measurements of non-commuting quantum observables are
possible at the cost of increased unsharpness or measurement uncertainty. Many
different criteria exist for defining what an "optimal" joint measurement is,
with corresponding different tradeoff relations for the measurements.
Understanding the limitations of such measurements is of fundamental interest
and relevant for quantum technology. Here, we experimentally test a tradeoff
relation for the sharpness of qubit measurements, a relation which refers
directly to the form of the measurement operators, rather than to errors in
estimates. We perform the first optical implementation of the simplest possible
optimal joint measurement, requiring less quantum resources than have
previously often been employed. Using a heralded single-photon source, we
demonstrate quantum-limited performance of the scheme on single quanta.
