论文标题
关于检测宏观叠加的硬度
On the Hardness of Detecting Macroscopic Superpositions
论文作者
论文摘要
何时“有效不可逆转”的融合？在这里，我们使用量子计算复杂性的工具来检查量子基础的中心问题。我们证明，如果一个人有一个量子电路来确定一个系统是否处于两个正交状态的叠加（例如，$ | $ | $ aclie $ \ \ rangle $ and $ | $ | $ | $ dead $ \ dead $ \ rangle $ ofschrödinger'scat），然后只有一个较大的电路，一个较大的电路，一个也可以$ \ mathit {swap {swap {swap {swap} $ dead cat a cat a cat a cat a cat a cat a cat a cat a cat a cat a cat a cat a cat a cat。换句话说，观察$ | $ Alive $ \ rangle $和$ | DEAD $ \ rangle $ States之间的干扰是一个“死灵 - - hard”问题，在任何死亡是永久性的世界上，从技术上讲都是不可行的。至于相反的语句（即交换的能力意味着检测干扰的能力），我们表明它具有单个例外，涉及（例如）（例如）Map $ | $ | $ | $ | $ | $ \ $ \ rangle $ to $ | $ | $ dead $ \ rangle $ \ rangle $，但$ | $ | $ | $ DEATH $ dead $ \ rangle \ $ | $ | $ | Alive $ \ rangle $ \ rangle $ \ rangle $ \ rangle $ \ rangle $。我们还表明，这些陈述是强大的---即使是$ \ mathit {partial} $观察干扰的能力意味着部分交换能力，反之亦然。最后，在不依赖任何未经证实的复杂性猜想的情况下，我们表明所有这些结果都在定量上很紧。我们的结果可能对可观察物在量子重力中的状态依赖性具有可能的影响，量子重力是最初激发了这项研究的主题。
When is decoherence "effectively irreversible"? Here we examine this central question of quantum foundations using the tools of quantum computational complexity. We prove that, if one had a quantum circuit to determine if a system was in an equal superposition of two orthogonal states (for example, the $|$Alive$\rangle$ and $|$Dead$\rangle$ states of Schrödinger's cat), then with only a slightly larger circuit, one could also $\mathit{swap}$ the two states (e.g., bring a dead cat back to life). In other words, observing interference between the $|$Alive$\rangle$and $|$Dead$\rangle$ states is a "necromancy-hard" problem, technologically infeasible in any world where death is permanent. As for the converse statement (i.e., ability to swap implies ability to detect interference), we show that it holds modulo a single exception, involving unitaries that (for example) map $|$Alive$\rangle$ to $|$Dead$\rangle$ but $|$Dead$\rangle$ to -$|$Alive$\rangle$. We also show that these statements are robust---i.e., even a $\mathit{partial}$ ability to observe interference implies partial swapping ability, and vice versa. Finally, without relying on any unproved complexity conjectures, we show that all of these results are quantitatively tight. Our results have possible implications for the state dependence of observables in quantum gravity, the subject that originally motivated this study.
