论文标题
将非本地游戏的近乎最佳量子策略四舍五入为使用最大纠缠状态的策略
Rounding near-optimal quantum strategies for nonlocal games to strategies using maximally entangled states
论文作者
论文摘要
我们为几个著名的非本地游戏家庭建立了近似刚度结果。特别是，我们表明，布尔约束系统（BCS）游戏接近完美的量子策略是相应的BCS代数的近似表示。同样，对于XOR非本地游戏类别，我们表明，近乎最佳的量子策略是与游戏最佳量子值相关的相应$*$ - 代数的近似表示。在这两种情况下，近似表示形式均相对于归一化的希尔伯特 - 施密特规范，并且独立于策略中使用的希尔伯特空间或量子状态。我们还表明，BCS（分别〜xor-elgebra）的近似表示会产生近乎完美的（分别是〜近距离的）量子策略的测量操作员，在该策略中，玩家在游戏中采用了最大的纠结状态。作为推论，每个接近完美的bcs（分别是近距离XOR）量子策略都接近使用最大纠缠状态的接近完美（分别〜近距离〜近距离）量子策略。最后，我们确定每个同步代数都是$*$ - 同构对某些BCS代数称为同步代数。这也使我们也可以将BCS刚度结果应用于同步游戏类别。
We establish approximate rigidity results for several well-known families of nonlocal games. In particular, we show that near-perfect quantum strategies for boolean constraint system (BCS) games are approximate representations of the corresponding BCS algebra. Likewise, for the class of XOR nonlocal games, we show that near-optimal quantum strategies are approximate representations of the corresponding $*$-algebra associated with optimal quantum values for the game. In both cases, the approximate representations are with respect to the normalized Hilbert-Schmidt norm and independent of the Hilbert space or quantum state employed in the strategy. We also show that approximate representation of the BCS (resp.~XOR-algebra) yields measurement operators for near-perfect (resp.~near-optimal) quantum strategies where the players employ a maximally entangled state in the game. As a corollary, every near-perfect BCS (resp.~near-optimal XOR) quantum strategy is close to a near-perfect (resp.~near-optimal) quantum strategy using a maximally entangled state. Lastly, we establish that every synchronous algebra is $*$-isomorphic to a certain BCS algebra called the SynchBCS algebra. This allows us to apply our BCS rigidity results to the class of synchronous games as well.
