纠缠辅助制备-测量随机访问码中的可验证量子优越性
Certified quantum supremacy in entanglement-assisted prepare-measure random-access-code
浏览论文内容
中文总结 AI 辅助
研究在 n→l 随机访问码框架下的纠缠辅助制备-测量通信游戏，通过分析技术得出 4→l、5→l 等情况下的最优量子成功概率，展示量子优越性，验证爱丽丝酉操作，还扩展了 n→n - 2 情况的量子优势证明。
中文摘要 AI 辅助
我们在发送方爱丽丝持有 n 位字符串并向接收方鲍勃通信 l < n 位或量子比特的 n→l 随机访问码（RAC）框架内，开发了一族涉及两方的半设备无关（SDI）纠缠辅助制备-测量（PM）通信游戏。与标准量子 PMRAC 不同，各方共享先验纠缠，爱丽丝对其子系统应用量子操作来编码输入并发送给鲍勃。我们首先考虑 l = 1 和 2 的 4→l 纠缠辅助 PMRAC，并使用一种优雅的分析技术得出最优量子成功概率，展示了相对于经典RAC和传统量子PMRAC的量子优越性，还表明最优量子优势可用于验证爱丽丝的酉操作。然后我们得出 l = 1、2 和 3 的 5→l 纠缠辅助 PMRAC 的量子成功概率上限。此外，我们还扩展了 n→n - 2 情况（n 为任意值）的量子优势证明。
英文摘要
We develop a family of semi-device-independent (SDI) entanglement-assisted prepare-measure (PM) communication games involving two parties, within the $n\rightarrow l$ random-access code (RAC) framework where the sender Alice holds a n-bit string and communicates $l<n$ bits or qubits to the receiver Bob. In contrast to the standard quantum PMRAC, here the parties share a prior entanglement, and Alice applies quantum operations on her sub-system to encode her inputs and sends to Bob. We first consider the $4\rightarrow l$ entanglement-assisted PMRAC with $l=1$ and $2$ and derive the optimal quantum success probabilities using an elegant analytical technique. We demonstrate quantum supremacy over both classical RACs and conventional quantum PMRACs. Moreover, we exhibit that the optimal quantum advantage allows one to certify Alice's unitary operations. We then derive an upper bound on the quantum success probabilities for $5\rightarrow l$ entanglement-assisted PMRAC with $l=1,2$ and $3$. Further, we extend the demonstration of quantum advantage for $n\rightarrow n-2$ case where n is arbitrary.
