We introduce witnesses for the average channel fidelity between a known target gate and an arbitrary unknown channel, for continuous-variable (CV) systems. These are observables whose expectation value yields a tight lower bound to the average channel fidelity in question, thus constituting a practical tool for certification of experimental CV gates. Our framework applies to a broad class of target gates. Here, we focus on three specific types of targets: multi-mode Gaussian unitary channels, single-mode coherent state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is a crucial ingredient for CV universal quantum computation. Our witnesses are experimentally-friendly as they rely exclusively on Gaussian measurements, even for the non-Gaussian-target case. Moreover, in all three cases, they can be measured efficiently in the estimation error ϵ and failure probability Δ, as well as in the number of modes m for the Gaussian-target case. To end up with, our approach for the Gaussian-target case relies on an improved measurement scheme for Gaussian state-fidelity witnesses, which is polynomially and exponentially more efficient in m and Δ, respectively, than previous schemes. The latter constitutes an interesting byproduct result on its own. Our findings are relevant to the experimental validation of many-body quantum technologies.

我们为连续变量 (CV) 系统引入了已知目标门和任意未知通道之间平均通道保真度的见证。这些是可观察值，其期望值对所讨论的平均通道保真度产生严格的下限，因此构成了验证实验 CV 门的实用工具。我们的框架适用于广泛的目标门。在这里，我们关注三种特定类型的目标：多模高斯单一通道、单模相干状态放大器和单模（非高斯）三次相位门，这是 CV 通用量子计算的关键组成部分。我们的见证人在实验上是友好的，因为他们完全依赖高斯测量，即使对于非高斯目标情况也是如此。此外，在所有三种情况下，ϵ和失败概率 Δ，以及高斯目标情况下的模式数m。最后，我们针对高斯目标情况的方法依赖于改进的高斯状态保真见证测量方案，与之前的方案相比，该方案在m和 Δ 方面分别以多项式和指数方式更有效。后者本身就构成了一个有趣的副产品结果。我们的发现与多体量子技术的实验验证有关。