论文标题
通过近似统一设计和有效的相对热化的高概率解耦
High probability decoupling via approximate unitary designs and efficient relative thermalisation
论文作者
论文摘要
我们证明，非催化脱钩是一个新的浓度结果，这表明，对于适当的$ t $，在量子系统上均匀地涂上统一选择的统一选择，从近似$ t $ design上均匀地施加，几乎是固定量子操作几乎脱离了固定的量子，然后具有很高的概率，从最初可能与之相关的另一个参考系统。较早的工作要么没有获得高脱钩概率，要么使用效率低下的单位，或者所需的催化纠缠才能解耦。相比之下，我们的近似统一设计始终保证与指数高的概率解耦，在某些条件下会导致计算有效的单位。结果，我们得出的结论是，在适当的条件下，有效实现的近似统一设计实现了量子热力学的相对热化，概率高。我们还显示了黑洞的争夺性属性，当黑洞的演化是根据伪随机的近似统一$ t $ - 设计的，而不是海顿·普雷斯基尔（Hayden-Preskill）先前考虑的HAAR随机进化。
We prove a new concentration result for non-catalytic decoupling by showing that, for suitably large $t$, applying a unitary chosen uniformly at random from an approximate $t$-design on a quantum system followed by a fixed quantum operation almost decouples, with high probability, the given system from another reference system to which it may initially have been correlated. Earlier works either did not obtain high decoupling probability, or used provably inefficient unitaries, or required catalytic entanglement for decoupling. In contrast, our approximate unitary designs always guarantee decoupling with exponentially high probability and, under certain conditions, lead to computationally efficient unitaries. As a result we conclude that, under suitable conditions, efficiently implementable approximate unitary designs achieve relative thermalisation in quantum thermodynamics with exponentially high probability. We also show the scrambling property of black hole, when the black hole evolution is according to pseudorandom approximate unitary $t$-design, as opposed to the Haar random evolution considered earlier by Hayden-Preskill.
