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arXiv 2401.01616quant-ph
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对于非正交QKD信号,最优集体测量能否优于个体测量?

Can optimal collective measurements outperform individual measurements for non-orthogonal QKD signals?

Isabella Cerutti, Petra F. Scudo

AI总结:

针对非正交QKD信号,基于算子代数和奇异值分解框架寻找最优测量,发现最优von Neumann测量优于POVMs,且集体测量不优于个体测量。

摘要:

我们研究了最优量子测量理论如何决定接收方在使用线性独立但非正交量子态的量子密钥分发(QKD)系统中所能获得的最大信息。这种设定是几种实用QKD协议的特征。由于非正交性,接收方无法无歧义地区分信号。为了理解这施加的基本限制,我们关注的量是发送方(Alice)与接收方之间的最大互信息,无论接收方是合法接收者(Bob)还是窃听者(Eve)。为寻找最优测量,我们使用基于算子代数的框架以及由奇异值分解导出的通用结果,实现了对von Neumann测量和正定算子值测量(POVMs)的最优解。针对两个信号详述的形式证明和定量分析表明,最优von Neumann测量是唯一确定的,且与POVMs相比能提供更高的信息增益。有趣的是,集体测量不仅没有比个体测量提供额外的信息增益,而且在POVMs情况下还会遭受增益降低。

英文摘要:

We consider how the theory of optimal quantum measurements determines the maximum information available to the receiving party of a quantum key distribution (QKD) system employing linearly independent but non-orthogonal quantum states. Such a setting is characteristic of several practical QKD protocols. Due to non-orthogonality, the receiver is not able to discriminate unambiguously between the signals. To understand the fundamental limits that this imposes, the quantity of interest is the maximum mutual information between the transmitter (Alice) and the receiver, whether legitimate (Bob) or an eavesdropper (Eve). To find the optimal measurement we use a framework based on operator algebra and general results derived from singular value decomposition, achieving optimal solutions for von Neumann measurements and positive operator-valued measures (POVMs). The formal proof and quantitative analysis elaborated for two signals allow one to conclude that optimal von Neumann measurements are uniquely defined and provide a higher information gain compared to POVMs. Interestingly, collective measurements not only do not provide additional information gain with respect to individual ones, but also suffer from a gain reduction in the case of POVMs.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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