信息论一次性程序：来自几何局域 $\text{QNC}_0$ 敌手
Information Theoretic One-Time Programs from Geometrically Local $\text{QNC}_0$ Adversaries
AI总结：
本文在几何局域量子电路约束下，利用随机线性码和量子随机访问码构建无需计算假设的模拟安全一次性存储器，并发展碰撞熵信息泄露界，但构造需解码随机码，非多项式时间。
摘要：
我们展示了如何在量子硬件受限的情况下，无需计算假设即可构建模拟安全的一次性存储器，从而构建一次性程序。具体而言，当受限于非自适应、恒定深度且为某个常数 $D$ 的 $D$ 维几何局域量子电路时，我们从随机线性码和量子随机访问码（QRAC）构建一次性存储器。我们对敌手的经典计算能力、可使用的量子比特数量或量子比特的相干时间不设任何限制。值得注意的是，只要输入量子比特以非容错方式编码（例如在非理想硬件中编码为高能态），即使在存在容错量子计算的情况下，我们的构造仍然可以是安全的。然而不幸的是，我们的构造需要解码随机线性码，因此不能在多项式时间内运行。我们留下一个开放问题：是否可以从几何局域量子电路构建多项式时间的信息论安全一次性存储器。\n可能具有独立意义的是，我们通过碰撞熵（2 阶 Renyi 熵）为信息泄露开发了一个进展界，以及为碰撞熵的“互信息”提供了一些关键技术引理。我们还开发了关于特定 $2 \mapsto 1$ QRAC 能泄露其输入多少信息的新界，这可能也具有独立意义。
英文摘要：
We show how to construct simulation secure one-time memories, and thus one-time programs, without computational assumptions in the presence of constraints on quantum hardware. Specifically, we build one-time memories from random linear codes and quantum random access codes (QRACs) when constrained to non-adaptive, constant depth, and $D$-dimensional geometrically-local quantum circuit for some constant $D$. We place no restrictions on the adversary's classical computational power, number of qubits it can use, or the coherence time of its qubits. Notably, our construction can still be secure even in the presence of fault tolerant quantum computation as long as the input qubits are encoded in a non-fault tolerant manner (e.g. encoded as high energy states in non-ideal hardware). Unfortunately though, our construction requires decoding random linear codes and thus does not run in polynomial time. We leave open the question of whether one can construct a polynomial time information theoretically secure one-time memory from geometrically local quantum circuits. Of potentially independent interest, we develop a progress bound for information leakage via collision entropy (Renyi entropy of order $2$) along with a few key technical lemmas for a "mutual information" for collision entropies. We also develop new bounds on how much information a specific $2 \mapsto 1$ QRAC can leak about its input, which may be of independent interest as well.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
