论文标题
量子算法随机性
Quantum algorithmic randomness
论文作者
论文摘要
Nies和Scholz引入了用于无限量子序列的量子Martin-Löf随机性（Q-MLR）。我们定义了量子solovay随机性的概念，该概念等效于Q-MLR。这样的证明通过子空间近似密度矩阵的纯线代数结果。然后，我们表明随机状态形成凸集。 Martin-Löf绝对连续性显示为Q-MLR的特殊情况。引入了量子shnorr随机性。显示大量定律的量子类似物可用于量子schnorr随机状态。
Quantum Martin-Löf randomness (q-MLR) for infinite qubit sequences was introduced by Nies and Scholz. We define a notion of quantum Solovay randomness which is equivalent to q-MLR. The proof of this goes through a purely linear algebraic result about approximating density matrices by subspaces. We then show that random states form a convex set. Martin-Löf absolute continuity is shown to be a special case of q-MLR. Quantum Schnorr randomness is introduced. A quantum analogue of the law of large numbers is shown to hold for quantum Schnorr random states.
