论文标题
计算量子相关性的条件熵
Computing conditional entropies for quantum correlations
论文作者
论文摘要
量子加密协议的速率通常是根据在一组量子状态下最小化的条件熵表示的。特别是，在与设备无关的环境中，最小化是在对手共同持有的所有量子状态下，而当事方与当事方所看到的统计数据一致。在这里，我们介绍了一种近似此类熵量的方法。应用于设备无关的随机性生成和量子密钥分布的设置，我们在各种设置中获得了协议速率的改进。特别是，我们发现执行与设备无关的量子键分布所需的最小全局检测效率的新上限，而无需额外的预处理。此外，我们表明我们的构建可以很容易地与熵积累定理相结合，以便为这些协议建立完整的有限键安全证明。为了实现这一目标，我们介绍了带有参数的迭代平均量子rényi分歧$α_k= 1+ \ frac {1} {1} {2^{k} -1} $，用于正整数$ k $。然后，我们表明，相应的条件熵承认了一种特别好的形式，在独立于设备的优化的背景下，可以使用Navascués-Pironio-Acín层次结构将其放松到半决赛编程问题。
The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum states jointly held by the adversary and the parties that are consistent with the statistics that are seen by the parties. Here, we introduce a method to approximate such entropic quantities. Applied to the setting of device-independent randomness generation and quantum key distribution, we obtain improvements on protocol rates in various settings. In particular, we find new upper bounds on the minimal global detection efficiency required to perform device-independent quantum key distribution without additional preprocessing. Furthermore, we show that our construction can be readily combined with the entropy accumulation theorem in order to establish full finite-key security proofs for these protocols. In order to achieve this we introduce the family of iterated mean quantum Rényi divergences with parameters $α_k = 1+\frac{1}{2^{k}-1}$ for positive integers $k$. We then show that the corresponding conditional entropies admit a particularly nice form which, in the context of device-independent optimization, can be relaxed to a semidefinite programming problem using the Navascués-Pironio-Acín hierarchy.
