The Gottesman-Knill theorem shows that Clifford circuits operating on stabilizer states can be efficiently simulated classically. However, in the setting of interactive protocols, it has remained unclear whether Clifford strategies with shared entanglement between provers offer any advantage over classical ones. We provide a negative answer to this question, demonstrating that even when Clifford provers are additionally allowed to perform general classical operations on measured qubits $-$ a computational model for which we introduce the complexity class $\text{Clifford-MIP}^\ast$ $-$ there is no advantage over classical strategies. Our results imply that $\text{Clifford-MIP}^\ast = \text{MIP}$. Furthermore, we utilize our findings to resolve an open question posed by Kalai et al. (STOC 2023). We show that quantum advantage in any non-local game requires at least two quantum provers operating outside the $\text{Clifford-MIP}^\ast$ computational model. This rules out a suggested approach for significantly improving the efficiency of tests for quantum advantage that are based on compiling non-local games.

翻译：Gottesman-Knill定理表明，作用于稳定子态的Clifford电路可以被经典计算机高效模拟。然而，在交互式协议场景中，拥有共享纠缠的Clifford策略是否比经典策略更具优势，这一问题始终悬而未决。我们对此给出了否定答案，证明了即使允许Clifford证明者额外对已测量量子比特执行任意经典操作——我们为此计算模型引入了复杂度类$\text{Clifford-MIP}^\ast$——其相对经典策略依然不存在任何优势。我们的结果表明$\text{Clifford-MIP}^\ast = \text{MIP}$。此外，我们利用这一发现解决了Kalai等人（STOC 2023）提出的一个开放性问题。我们证明在任何非局域博弈中实现量子优势，至少需要两个在$\text{Clifford-MIP}^\ast$计算模型之外运行的量子证明者。这排除了通过编译非局域博弈来显著提升量子优势测试效率的可能途径。