信息泄漏的量子优势
Quantum Advantage on Information Leakage for Equality
摘要：
我们证明了一个下界的信息泄漏的任何经典协议计算等式功能的同时消息传递（SMP）模型。我们的界限是有效的，在有限长度制度，是强大的，足以证明量子优势，在实际的量子协议的信息泄漏。我们证明了我们的界限，通过获得一个改进的有限大小版本的通信界由于Babai和Kimmel，随机通信的SMP模型中的确定性通信。然后，我们通过一系列的减少信息泄漏随机通信。我们首先提供了信息泄漏的替代表征，使我们能够将其链接到平均长度的通信，同时允许共享的随机性（成对的，与裁判）。马尔可夫不等式将其与有限长度通信联系起来，纽曼类型的参数允许我们从共享随机性到私有随机性。唯一的减少，我们招致超过一个对数加法因子是在马尔可夫不等式，特别是，我们的压缩方法基本上是紧密的SMP模型与平均长度的通信。
英文摘要：
We prove a lower bound on the information leakage of any classical protocol computing the equality function in the simultaneous message passing (SMP) model. Our bound is valid in the finite length regime and is strong enough to demonstrate a quantum advantage in terms of information leakage for practical quantum protocols. We prove our bound by obtaining an improved finite size version of the communication bound due to Babai and Kimmel, relating randomized communication to deterministic communication in the SMP model. We then relate information leakage to randomized communication through a series of reductions. We first provide alternative characterizations for information leakage, allowing us to link it to average length communication while allowing for shared randomness (pairwise, with the referee). A Markov inequality links this with bounded length communication, and a Newman type argument allows us to go from shared to private randomness. The only reduction in which we incur more than a logarithmic additive factor is in the Markov inequality; in particular, our compression method is essentially tight for the SMP model with average length communication.
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