在玻色通道上实现隐蔽通信与传感的隐秘信号
Covert Signaling for Communication and Sensing over the Bosonic Channels
AI总结：
研究了在有损耗热噪声玻色通道上稀疏信号的隐蔽通信与传感，发现最优量子态为两个连续光子数态的混合，揭示了隐蔽性与性能之间的权衡。
摘要：
防止信号检测在通信和主动传感中需要仔细控制传输功率。实际上，隐蔽经典和量子通信与传感的平方根定律（SRL）规定，平均输出功率每通道使用量随n通道使用量呈1/√n比例下降。两种实现策略为扩散信号和稀疏信号。前者在所有n通道使用中以1/√n衰减功率传输，便于数学分析。后者在大约√n次通道使用中以恒定功率传输，其余时间保持沉默。这在与现代数字发射机兼容性方面具有显著实际优势。本文研究了稀疏信号在有损耗热噪声玻色通道上的表现，这些通道描述了量子上许多实际通道（包括光、微波和射频）。我们确定了最小可检测性输入信号状态。发现了一个非直观的最优量子态结构：仅两个连续光子数态的混合。特别是，在低亮度范围内，最优信号态是真空和单光子态的混合。由于这些态在通信和主动传感中通常不理想，我们探讨了由此产生的权衡，并确定了输入功率阈值，用于在优化隐蔽性与通信和传感任务性能之间进行转换。
英文摘要：
Preventing signal detection in communication and active sensing requires careful control of transmission power. In fact, the square-root laws (SRL) for covert classical and quantum communication and sensing prescribe that the average output energy per channel use scales as $1/\sqrt{n}$ for $n$ channel uses. \emph{Diffuse} and \emph{sparse} signaling achieve this. The former transmits signals whose energy decays as $1/\sqrt{n}$ over all $n$ channel uses, which is convenient for mathematical analysis. The latter transmits constant-energy signals only approximately $\propto\sqrt{n}$ times out of $n$ channel uses, remaining silent on the others. This offers significant practical advantages in compatibility with modern digital transmitters. Here, we study sparse signaling over the lossy thermal-noise bosonic channel, which is a quantum model of many practical channels (including optical, microwave, and radio-frequency). We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon. Since these states are generally suboptimal for both communication and active sensing, we explore the resulting trade-off and identify input-power thresholds for transitions between optimizing covertness and performance in communication and sensing tasks.
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