论文标题
带有量子侧信息的猜测
Guesswork with Quantum Side Information
论文作者
论文摘要
平均需要多少猜测才能正确猜测随机变量的实现？这个问题的答案导致了梅西在1994年引入了称为猜测的数量的概念，可以将其视为熵的替代安全标准。在本文中，我们考虑在存在量子侧信息的情况下的猜测，并表明一般的顺序猜测策略等同于进行单个测量并从结果中选择猜测策略。我们使用此结果在存在量子侧信息的情况下推断出猜测的熵一声和渐近界限，并制定半明确程序（SDP）以计算数量。我们在数值和分析上评估了一个涉及BB84状态的简单示例的猜测，并证明了连续性结果，该结果在将猜测用作安全标准时证明了稍微不完美的密钥状态的安全性。
What is the minimum number of guesses needed on average to correctly guess a realization of a random variable? The answer to this question led to the introduction of the notion of a quantity called guesswork by Massey in 1994, which can be viewed as an alternate security criterion to entropy. In this paper, we consider the guesswork in the presence of quantum side information, and show that a general sequential guessing strategy is equivalent to performing a single measurement and choosing a guessing strategy from the outcome. We use this result to deduce entropic one-shot and asymptotic bounds on the guesswork in the presence of quantum side information, and to formulate a semi-definite program (SDP) to calculate the quantity. We evaluate the guesswork for a simple example involving the BB84 states, both numerically and analytically, and prove a continuity result that certifies the security of slightly imperfect key states when the guesswork is used as the security criterion.
