在有界经典通信下认证测量不相容性
Certifying Measurement Incompatibility under Bounded Classical Communication
- Institute for Information Processing (tnt/L3S)（信息处理研究所）
- Leibniz Universität Hannover（汉诺威莱布尼茨大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对有界经典通信下认证测量不相容性的问题，引入并集最大泄漏量化观测概率的共同经典解释所需信息，通过线性规划计算，证明其与经典通信比特数及纠缠的关系，并用于认证随机性私密性。
AI中文摘要：
测量不相容性使得量子在通信和态判别中具有优势。它也是贝尔非局域性的必要条件，而贝尔非局域性用于量子密钥分发和私有随机生成的设备无关协议。经典通信会影响接收方的结果，因此在认证测量不相容性时必须考虑经典通信。我们引入了并集最大泄漏，它量化了所有观测概率的共同经典解释所需的信息量，并通过线性规划从这些概率中计算得出。如果在接收方独立选择测量之前有一条至多$k$比特的消息，则每条消息的相容测量给出的并集最大泄漏至多为$k$。这个界对任何与输入无关的非信号共享资源都成立。在量子理论中，违反该界也意味着初始共享态是纠缠的。反之，并集最大泄漏决定了用相容测量和任意非信号辅助重现观测所需的最小经典通信量。对于固定的共享量子态和接收方测量，当且仅当对于某个消息值，接收方的测量相对于该态上的二值发送方测量是贝尔非局域的，才可能发生违反。对于二值接收方结果，我们证明违反也认证了相对于发送方私有的随机性，即使接收方的测量依赖于发送方的消息且发送方保留量子侧信息。我们通过一个显式的条件熵界量化了这种隐私性，并在具有设备记忆的顺序协议中建立了可组合安全的随机提取。
英文摘要：
Measurement incompatibility enables quantum advantages in communication and state discrimination. It is also necessary for Bell nonlocality, which is used in device-independent protocols for quantum key distribution and private randomness generation. Classical communication can influence the receiver's outcome and must therefore be accounted for when certifying measurement incompatibility. We introduce union maximal leakage, which quantifies the information needed for a common classical explanation of all observed probabilities and is computed from them by a linear program. If a message of at most $k$ bits precedes the receiver's independent measurement choice, compatible measurements for each message give union maximal leakage at most $k$. This bound holds with any input-independent nonsignalling shared resource. In quantum theory, a violation also implies that the initially shared state is entangled. Conversely, union maximal leakage determines the minimum classical communication needed to reproduce the observations with compatible measurements and arbitrary nonsignalling assistance. For a fixed shared quantum state and receiver measurements, a violation is possible exactly when, for some message value, the receiver's measurements are Bell-nonlocal against two-outcome sender measurements on that state. For binary receiver outcomes, we show that a violation also certifies randomness private from the sender, even when the receiver's measurement depends on the sender's message and the sender retains quantum side information. We quantify this privacy through an explicit conditional entropy bound and establish composably secure randomness extraction in sequential protocols with device memory.
