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.
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