  The measurement of a quantum system is often performed by encoding its state
in a single observable of a light field. The measurement efficiency of this
observable can be reduced by loss or excess noise on the way to the detector.
Even a \textit{quantum-limited} detector that simultaneously measures a second
non-commuting observable would double the output noise, therefore limiting the
efficiency to $50\%$. At microwave frequencies, an ideal measurement efficiency
can be achieved by noiselessly amplifying the information-carrying quadrature
of the light field, but this has remained an experimental challenge. Indeed,
while state-of-the-art Josephson-junction based parametric amplifiers can
perform an ideal single-quadrature measurement, they require lossy ferrite
circulators in the signal path, drastically decreasing the overall efficiency.
In this paper, we present a nonreciprocal parametric amplifier that combines
single-quadrature measurement and directionality without the use of strong
external magnetic fields. We extract a measurement efficiency of $62_{-9}^{+17}
\%$ that exceeds the quantum limit and that is not limited by fundamental
factors. The amplifier can be readily integrated with superconducting devices,
creating a path for ideal measurements of quantum bits and mechanical
oscillators.
