AI 中文总结
该研究证明玻色热衰减器的单模高斯态相干信息下界为精确上确界，发现非高斯输入可提升相干信息，在η=0.7841时证实量子容量为正，确定了玻色量子通信可行的新高噪声区域。
AI 中文摘要
玻色热衰减器的量子容量由其相干信息的正则化给出，目前仍是未知的。Holevo和Werner在1999年的开创性工作建立了从输入热态得到的标准单次使用下界。我们首先证明，这个长期存在的下界是所有单模高斯态上的精确上确界，随后表明，关键在于非高斯态可以表现得更好。因此，我们证明了在信道非反退化的参数区域中量子容量为正，而在该区域中对单模高斯态优化的相干信息消失。例如，当环境中有1个热光子且透射率η=0.8时，每个单模高斯输入的相干信息均非正。我们给出了一个明确的秩2非高斯态，仅支撑在6个福克能级上，其相干信息被证实至少为每次信道使用4.7×10⁻⁴量子比特。这个简短的见证远非数值最优：在相同参数下，对固定非高斯族的数值优化达到至少8.4×10⁻³量子比特每次信道使用。更一般地，在ν=1时，使用非高斯输入我们证实相干信息为正，因此量子容量为正，直至η=0.7841；相比之下，当η≤0.75时，该信道是反退化的，因此量子容量为零。总体而言，我们的工作确定了玻色量子通信可行的新的高噪声区域。
英文摘要
The quantum capacity of the bosonic thermal attenuator, which is given by the regularization of its coherent information, is unknown. The seminal work of Holevo and Werner established in 1999 the standard one-use lower bound obtained from input thermal states. We first prove that this long-standing lower bound is the exact supremum over all single-mode Gaussian states and then show that, crucially, a non-Gaussian state can do better. As a consequence, we prove positivity of the quantum capacity in a parameter region where the channel is not antidegradable, yet its coherent information optimized over single-mode Gaussian states vanishes. For example, with one thermal photon in the environment and at transmissivity $η=0.8$, the coherent information is non-positive for every single-mode Gaussian input. We give an explicit rank-two non-Gaussian state, supported on only six Fock levels, whose coherent information is certified to be at least $4.7\times10^{-4}$ qubits per channel use. This short witness is far from numerically optimal: a numerical optimization over fixed non-Gaussian families reaches at least $8.4\times 10^{-3}$ qubits per channel use at the same point. More generally, at $ν=1$, using non-Gaussian inputs we certify positivity of the coherent information, and therefore of the quantum capacity, down to $η=0.7841$; by contrast, the channel is antidegradable, and hence has zero quantum capacity, for $η\leq0.75$. Overall, our work identifies new high-noise regimes in which bosonic quantum communication is possible.
Comments6 + 5 pages, 2 figures
