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The low-noise amplification of weak microwave signals is crucial forcountless protocols in quantum information processing. Quantum mechanics setsan ultimate lower limit of half a photon to the added input noise forphase-preserving amplification of narrowband signals, also known as thestandard quantum limit (SQL). This limit, which is equivalent to a maximumquantum efficiency of $0.5$, can be overcome by employing nondegenerateparametric amplification of broadband signals. We show that, in principle, amaximum quantum efficiency of 1 can be reached. Experimentally, we find aquantum efficiency of $0.69 \pm 0.02$, well beyond the SQL, by employing aflux-driven Josephson parametric amplifier and broadband thermal signals. Weexpect that our results allow for fundamental improvements in the detection ofultraweak microwave signals.

Beyond the standard quantum limit of parametric amplification