发表机构
CNRS; INRIA; University of Ottawa（法国国家科学研究中心; 法国国家信息与自动化研究所; 渥太华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明三次高斯态的Wigner负性越大，退相干时间越短（上界为负性的平方倒数），并给出达到该上界的最优态及其制备条件，同时与Fock态比较了退相干和纠缠潜力。
AI 中文摘要
Wigner负性已被证明是量子计算中的一种资源，这引发了如何高效制备具有大Wigner负性的态的问题。三次高斯态（通过对高斯态施加三次门而获得）已被提出作为此目的的候选态。我们证明，具有大Wigner负性$\mathcal N$的三次高斯态必然具有较短的退相干时间$\tau$，且$\tau$的上界为$\mathcal N^{-2}$。换言之，大的Wigner负性是有代价的：三次高斯态的退相干时间$\tau$至少随负性$\mathcal N$的平方而减少。在固定Wigner负性$\mathcal N$下最大化$\tau$，我们证明该上界可由最优三次高斯态达到。这些态具有如下性质：对于大负性，最优压缩按$\ln\mathcal N$缩放，最优三次性按$\mathcal N^{-1}$缩放。因此，具有大负性的最优三次高斯态可以通过施加足够的压缩，以较小的三次性来构造。然而，它们的退相干时间随负性的增加而减少。此外，我们证明它们的制备对热噪声极其敏感。最后，对于每个整数$n$，我们将最优三次高斯态与具有相同负性的第$n$个Fock态进行比较：尽管它们在光子数分布和Wigner函数上存在显著差异，我们证明它们具有相似的（尽管略大）退相干时间和通过分束器的纠缠产生潜力。
英文摘要
Wigner negativity has been shown to be a resource in quantum computing, raising the question of how to efficiently produce states with a large Wigner negativity. Cubic Gaussian states, obtained when a cubic gate is applied to a Gaussian state, have been proposed as candidates for this purpose. We show that cubic Gaussian states with a large Wigner negativity $\mathcal N$ necessarily have a short decoherence time $τ$ that is bounded above by $\mathcal N^{-2}$. In other words, a large Wigner negativity comes at a cost: the decoherence time $τ$ of cubic Gaussian states decreases at least quadratically in the negativity $\mathcal N$. Maximizing $τ$ at fixed Wigner negativity $\mathcal N$, we show that this upper bound is reached by optimal cubic Gaussian states. They have the property that for large negativity, the optimal squeezing scales as $\ln\mathcal N$ and the optimal cubicity as $\mathcal N^{-1}$. Optimal cubic Gaussian states with large negativity can therefore be constructed with small cubicity, provided sufficient squeezing is applied. However, their decoherence time decreases with growing negativity. In addition, we show that their preparation is extremely sensitive to thermal noise. Finally, we compare, for each integer $n$, the optimal cubic Gaussian state with the $n$th Fock state that has the same negativity: despite their pronounced differences in photon number distribution and Wigner function, we show that they have similar, be it slightly larger, decoherence times and entanglement generating potential through a beam splitter.
Comments32 pages, 9 figures
