量子交互作用可以在并行重复下超激活作弊
Quantum interaction can superactivate cheating under parallel repetition
- University of Ottawa（渥太华大学）
- University of Copenhagen（哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究揭示量子通信可使并行重复在特定游戏中超激活作弊，即单实例局部值小于1但重复后等于1，并证明纠缠辅助零误差容量不可超激活。
AI中文摘要：
我们研究交互式多证明者游戏和多轮协议，其中验证者与证明者之间的通信是量子的。已知并行重复可以将经典双证明者游戏的可靠性误差任意抑制到接近零，如Raz（STOC '95）所示，即使采用量子策略也是如此，如Yuen（ICALP '16）以及Bavarian、Vidick和Yuen（STOC '17）所示。然而，我们表明量子通信可以产生相反且出乎意料的效果。具体而言，我们展示了一个单轮量子游戏和两轮QMIP协议，其局部（非纠缠）值对于单个实例严格小于1，但在n重并行重复下对于每个n≥2却等于1。关键在于并行重复不仅施加了额外的获胜条件，还提供了额外的量子资源，因为交换状态中的纠缠可以跨副本联合利用。我们的多轮示例建立在量子信道零误差容量的超激活之上。为了建立这种联系，我们引入了量子游戏和交互式协议，它们捕捉了单次零误差经典和量子容量，无论有无纠缠辅助。我们的构造使用量子态验证和基于隐形传态的从两轮到一轮的归约。相反，当允许共享纠缠时，我们表明在最多交换3条消息的情况下，并行重复不能增加纠缠值，这与Bellare、Impagliazzo和Naor（FOCS '97）的经典结果以及Kitaev和Watrous（STOC '00）的单证明者系统结果一致。将此单调性与我们的量子游戏-信道对应关系相结合，我们表明纠缠辅助的零误差经典和量子容量不能被超激活。
英文摘要：
We study interactive multiprover games and many-round protocols in which the communication between the verifier and the provers is quantum. Parallel repetition is known to suppress soundness error of classical two-prover games arbitrarily close to zero, as shown by Raz (STOC '95), even with quantum strategies as shown by Yuen (ICALP '16), and Bavarian, Vidick and Yuen (STOC '17). Yet, we show that quantum communication can have the opposite, unexpected effect. Specifically, we exhibit a one-round quantum game and two-round $\mathsf{QMIP}$ protocols whose local (unentangled) value is strictly less than one for a single instance, yet equals one under $n$-fold parallel repetition for every $n \geq 2$. The key is that parallel repetition not only imposes additional winning conditions but also supplies additional quantum resources as entanglement in the exchanged states can be exploited jointly across copies. Our multiround examples build on superactivation of zero-error capacities of quantum channels. To establish this connection, we introduce quantum games and interactive protocols which capture the one-shot zero-error classical and quantum capacities, both with and without entanglement assistance. Our constructions use quantum-state verification and a teleportation-based reduction from two rounds to one. In contrast, when shared entanglement is allowed, we show that parallel repetition cannot increase the entangled value when at most $3$ messages are exchanged, consistent with classical results of Bellare, Impagliazzo and Naor (FOCS '97), and that of single-prover systems by Kitaev and Watrous (STOC '00). Combining this monotonicity with our quantum game-channel correspondence, we show that entanglement-assisted zero-error classical and quantum capacities cannot be superactivated.
