论文标题
部分可观测时空混沌系统的无模型预测
Irreducible magic sets for $n$-qubit systems
论文作者
论文摘要
观察物的魔术集是最小的结构，可捕获$ n \ ge 2 $ Qubits系统的量子状态无关的优势，因此是研究经典物理和量子物理之间接口的基本工具。 Arkhipov的定理（Arxiv：1209.3819）指出，$ n $ qubit的魔法集可以将每个观察到的恰好在两个兼容可观察物中的子集中缩小到两个Qubit的魔术方形或三Qubit的魔术pentagram [N。 D. Mermin，物理。莱特牧师。 65，3373（1990）]。一个开放的问题是，是否有魔术集无法简化为广场或五角星。如果它们存在，第二个关键问题是它们是否需要$ n> 3 $ QUBITS，因为，如果是这种情况，这些魔术集将捕获最小状态独立的量子优势，该量子的特定于$ n $ qubit的系统，其特定值为$ n $。在这里，我们肯定地回答了这两个问题。我们确定无法将其简化为广场或五角星的魔术集，需要$ n = 3,4,5 $或$ 6 $ QUBITS。此外，我们证明了Arkhipov的定理的广义版本，给定超图提供了一种有效的算法，决定它是否可以容纳魔术集，并解决了另一个开放问题，即给定魔术集，获得了其相关的非上隐性性不平等的紧密界限。
Magic sets of observables are minimal structures that capture quantum state-independent advantage for systems of $n\ge 2$ qubits and are, therefore, fundamental tools for investigating the interface between classical and quantum physics. A theorem by Arkhipov (arXiv:1209.3819) states that $n$-qubit magic sets in which each observable is in exactly two subsets of compatible observables can be reduced either to the two-qubit magic square or the three-qubit magic pentagram [N. D. Mermin, Phys. Rev. Lett. 65, 3373 (1990)]. An open question is whether there are magic sets that cannot be reduced to the square or the pentagram. If they exist, a second key question is whether they require $n >3$ qubits, since, if this is the case, these magic sets would capture minimal state independent quantum advantage that is specific for $n$-qubit systems with specific values of $n$. Here, we answer both questions affirmatively. We identify magic sets which cannot be reduced to the square or the pentagram and require $n=3,4,5$, or $6$ qubits. In addition, we prove a generalized version of Arkhipov's theorem providing an efficient algorithm for, given a hypergraph, deciding whether or not it can accommodate a magic set, and solve another open problem, namely, given a magic set, obtaining the tight bound of its associated noncontextuality inequality.
