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arXiv 2008.06205quant-phgr-qc
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因果序叠加的一个No-Go定理

A no-go theorem for superpositions of causal orders

Fabio Costa

摘要:

事件的因果顺序不需要固定:一辆公共汽车是在另一辆公共汽车之前还是之后到达某个车站,可以取决于其他变量,比如交通。因果顺序的相干量子控制也是可能的,并且是几项任务的有用资源。然而,量子控制意味着一个控制系统携带着哪个顺序的信息--如果控制被追踪,事件的顺序仍然是概率混合。两个事件的顺序是否可以是纯粹的叠加,与任何其他系统无关?在这里,我们表明,这是不可能的广泛的一类过程:一个纯粹的叠加的任何一对马尔可夫,酉过程具有相同的局部尺寸和不同的因果顺序是不是一个有效的过程,即它的结果在非正规化的概率时,探测某些操作。这一结果对量子信息处理的新资源和量子引力理论中可能的过程施加了限制。

英文摘要:

The causal order of events need not be fixed: whether a bus arrives before or after another at a certain stop can depend on other variables -- like traffic. Coherent quantum control of causal order is possible too and is a useful resource for several tasks. However, quantum control implies that a controlling system carries the which-order information -- if the control is traced out, the order of events remains in a probabilistic mixture. Can the order of two events be in a pure superposition, uncorrelated with any other system? Here we show that this is not possible for a broad class of processes: a pure superposition of any pair of Markovian, unitary processes with equal local dimensions and different causal orders is not a valid process, namely it results in non-normalised probabilities when probed with certain operations. The result imposes constraints on novel resources for quantum information processing and on possible processes in a theory of quantum gravity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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